More on Marketing

Rachel Greenberg
3 years ago
6 Causes Your Sales Pitch Is Unintentionally Repulsing Customers
Skip this if you don't want to discover why your lively, no-brainer pitch isn't making $10k a month.
You don't want to be repulsive as an entrepreneur or anyone else. Making friends, influencing people, and converting strangers into customers will be difficult if your words evoke disgust, distrust, or disrespect. You may be one of many entrepreneurs who do this obliviously and involuntarily.
I've had to master selling my skills to recruiters (to land 6-figure jobs on Wall Street), selling companies to buyers in M&A transactions, and selling my own companies' products to strangers-turned-customers. I probably committed every cardinal sin of sales repulsion before realizing it was me or my poor salesmanship strategy.
If you're launching a new business, frustrated by low conversion rates, or just curious if you're repelling customers, read on to identify (and avoid) the 6 fatal errors that can kill any sales pitch.
1. The first indication
So many people fumble before they even speak because they assume their role is to convince the buyer. In other words, they expect to pressure, arm-twist, and combat objections until they convert the buyer. Actuality, the approach stinks of disgust, and emotionally-aware buyers would feel "gross" immediately.
Instead of trying to persuade a customer to buy, ask questions that will lead them to do so on their own. When a customer discovers your product or service on their own, they need less outside persuasion. Why not position your offer in a way that leads customers to sell themselves on it?
2. A flawless performance
Are you memorizing a sales script, tweaking video testimonials, and expunging historical blemishes before hitting "publish" on your new campaign? If so, you may be hurting your conversion rate.
Perfection may be a step too far and cause prospects to mistrust your sincerity. Become a great conversationalist to boost your sales. Seriously. Being charismatic is hard without being genuine and showing a little vulnerability.
People like vulnerability, even if it dents your perfect facade. Show the customer's stuttering testimonial. Open up about your or your company's past mistakes (and how you've since improved). Make your sales pitch a two-way conversation. Let the customer talk about themselves to build rapport. Real people sell, not canned scripts and movie-trailer testimonials.
If marketing or sales calls feel like a performance, you may be doing something wrong or leaving money on the table.
3. Your greatest phobia
Three minutes into prospect talks, I'd start sweating. I was talking 100 miles per hour, covering as many bases as possible to avoid the ones I feared. I knew my then-offering was inadequate and my firm had fears I hadn't addressed. So I word-vomited facts, features, and everything else to avoid the customer's concerns.
Do my prospects know I'm insecure? Maybe not, but it added an unnecessary and unhelpful layer of paranoia that kept me stressed, rushed, and on edge instead of connecting with the prospect. Skirting around a company, product, or service's flaws or objections is a poor, temporary, lazy (and cowardly) decision.
How can you project confidence and trust if you're afraid? Before you make another sales call, face your shortcomings, weak points, and objections. Your company won't be everyone's cup of tea, but you should have answers to every question or objection. You should be your business's top spokesperson and defender.
4. The unintentional apologies
Have you ever begged for a sale? I'm going to say no, however you may be unknowingly emitting sorry, inferior, insecure energy.
Young founders, first-time entrepreneurs, and those with severe imposter syndrome may elevate their target customer. This is common when trying to get first customers for obvious reasons.
Since you're truly new at this, you naturally lack experience.
You don't have the self-confidence boost of thousands or hundreds of closed deals or satisfied client results to remind you that your good or service is worthwhile.
Getting those initial few clients seems like the most difficult task, as if doing so will decide the fate of your company as a whole (it probably won't, and you shouldn't actually place that much emphasis on any one transaction).
Customers can smell fear, insecurity, and anxiety just like they can smell B.S. If you believe your product or service improves clients' lives, selling it should feel like a benevolent act of service, not a sleazy money-grab. If you're a sincere entrepreneur, prospects will believe your proposition; if you're apprehensive, they'll notice.
Approach every sale as if you're fine with or without it. This has improved my salesmanship, marketing skills, and mental health. When you put pressure on yourself to close a sale or convince a difficult prospect "or else" (your company will fail, your rent will be late, your electricity will be cut), you emit desperation and lower the quality of your pitch. There's no point.
5. The endless promises
We've all read a million times how to answer or disprove prospects' arguments and add extra incentives to speed or secure the close. Some objections shouldn't be refuted. What if I told you not to offer certain incentives, bonuses, and promises? What if I told you to walk away from some prospects, even if it means losing your sales goal?
If you market to enough people, make enough sales calls, or grow enough companies, you'll encounter prospects who can't be satisfied. These prospects have endless questions, concerns, and requests for more, more, more that you'll never satisfy. These people are a distraction, a resource drain, and a test of your ability to cut losses before they erode your sanity and profit margin.
To appease or convert these insatiably needy, greedy Nellies into customers, you may agree with or acquiesce to every request and demand — even if you can't follow through. Once you overpromise and answer every hole they poke, their trust in you may wane quickly.
Telling a prospect what you can't do takes courage and integrity. If you're honest, upfront, and willing to admit when a product or service isn't right for the customer, you'll gain respect and positive customer experiences. Sometimes honesty is the most refreshing pitch and the deal-closer.
6. No matter what
Have you ever said, "I'll do anything to close this sale"? If so, you've probably already been disqualified. If a prospective customer haggles over a price, requests a discount, or continues to wear you down after you've made three concessions too many, you have a metal hook in your mouth, not them, and it may not end well. Why?
If you're so willing to cut a deal that you cut prices, comp services, extend payment plans, waive fees, etc., you betray your own confidence that your product or service was worth the stated price. They wonder if anyone is paying those prices, if you've ever had a customer (who wasn't a blood relative), and if you're legitimate or worth your rates.
Once a prospect senses that you'll do whatever it takes to get them to buy, their suspicions rise and they wonder why.
Why are you cutting pricing if something is wrong with you or your service?
Why are you so desperate for their sale?
Why aren't more customers waiting in line to pay your pricing, and if they aren't, what on earth are they doing there?
That's what a prospect thinks when you reveal your lack of conviction, desperation, and willingness to give up control. Some prospects will exploit it to drain you dry, while others will be too frightened to buy from you even if you paid them.
Walking down a two-way street. Be casual.
If we track each act of repulsion to an uneasiness, fear, misperception, or impulse, it's evident that these sales and marketing disasters were forced communications. Stiff, imbalanced, divisive, combative, bravado-filled, and desperate. They were unnatural and accepted a power struggle between two sparring, suspicious, unequal warriors, rather than a harmonious oneness of two natural, but opposite parties shaking hands.
Sales should be natural, harmonious. Sales should feel good for both parties, not like one party is having their arm twisted.
You may be doing sales wrong if it feels repulsive, icky, or degrading. If you're thinking cringe-worthy thoughts about yourself, your product, service, or sales pitch, imagine what you're projecting to prospects. Don't make it unpleasant, repulsive, or cringeworthy.

Rita McGrath
3 years ago
Flywheels and Funnels
Traditional sales organizations used the concept of a sales “funnel” to describe the process through which potential customers move, ending up with sales at the end. Winners today have abandoned that way of thinking in favor of building flywheels — business models in which every element reinforces every other.
Ah, the marketing funnel…
Prospective clients go through a predictable set of experiences, students learn in business school marketing classes. It looks like this:
Understanding the funnel helps evaluate sales success indicators. Gail Goodwin, former CEO of small business direct mail provider Constant Contact, said managing the pipeline was key to escaping the sluggish SaaS ramp of death.
Like the funnel concept. To predict how well your business will do, measure how many potential clients are aware of it (awareness) and how many take the next step. If 1,000 people heard about your offering and 10% showed interest, you'd have 100 at that point. If 50% of these people made buyer-like noises, you'd know how many were, etc. It helped model buying trends.
TV, magazine, and radio advertising are pricey for B2C enterprises. Traditional B2B marketing involved armies of sales reps, which was expensive and a barrier to entry.
Cracks in the funnel model
Digital has exposed the funnel's limitations. Hubspot was born at a time when buyers and sellers had huge knowledge asymmetries, according to co-founder Brian Halligan. Those selling a product could use the buyer's lack of information to become a trusted partner.
As the world went digital, getting information and comparing offerings became faster, easier, and cheaper. Buyers didn't need a seller to move through a funnel. Interactions replaced transactions, and the relationship didn't end with a sale.
Instead, buyers and sellers interacted in a constant flow. In many modern models, the sale is midway through the process (particularly true with subscription and software-as-a-service models). Example:
You're creating a winding journey with many touch points, not a funnel (and lots of opportunities for customers to get lost).
From winding journey to flywheel
Beyond this revised view of an interactive customer journey, a company can create what Jim Collins famously called a flywheel. Imagine rolling a heavy disc on its axis. The first few times you roll it, you put in a lot of effort for a small response. The same effort yields faster turns as it gains speed. Over time, the flywheel gains momentum and turns without your help.
Modern digital organizations have created flywheel business models, in which any additional force multiplies throughout the business. The flywheel becomes a force multiplier, according to Collins.
Amazon is a famous flywheel example. Collins explained the concept to Amazon CEO Jeff Bezos at a corporate retreat in 2001. In The Everything Store, Brad Stone describes in his book The Everything Store how he immediately understood Amazon's levers.
The result (drawn on a napkin):
Low prices and a large selection of products attracted customers, while a focus on customer service kept them coming back, increasing traffic. Third-party sellers then increased selection. Low-cost structure supports low-price commitment. It's brilliant! Every wheel turn creates acceleration.
Where from here?
Flywheel over sales funnel! Consider these business terms.

Joseph Mavericks
3 years ago
You Don't Have to Spend $250 on TikTok Ads Because I Did
900K impressions, 8K clicks, and $$$ orders…
I recently started dropshipping. Now that I own my business and can charge it as a business expense, it feels less like money wasted if it doesn't work. I also made t-shirts to sell. I intended to open a t-shirt store and had many designs on a hard drive. I read that Tiktok advertising had a high conversion rate and low cost because they were new. According to many, the advertising' cost/efficiency ratio would plummet and become as bad as Google or Facebook Ads. Now felt like the moment to try Tiktok marketing and dropshipping. I work in marketing for a SaaS firm and have seen how poorly ads perform. I wanted to try it alone.
I set up $250 and ran advertising for a week. Before that, I made my own products, store, and marketing. In this post, I'll show you my process and results.
Setting up the store
Dropshipping is a sort of retail business in which the manufacturer ships the product directly to the client through an online platform maintained by a seller. The seller takes orders but has no stock. The manufacturer handles all orders. This no-stock concept increases profitability and flexibility.
In my situation, I used previous t-shirt designs to make my own product. I didn't want to handle order fulfillment logistics, so I looked for a way to print my designs on demand, ship them, and handle order tracking/returns automatically. So I found Printful.
I needed to connect my backend and supplier to a storefront so visitors could buy. 99% of dropshippers use Shopify, but I didn't want to master the difficult application. I wanted a one-day project. I'd previously worked with Big Cartel, so I chose them.
Big Cartel doesn't collect commissions on sales, simply a monthly flat price ($9.99 to $19.99 depending on your plan).
After opening a Big Cartel account, I uploaded 21 designs and product shots, then synced each product with Printful.
Developing the ads
I mocked up my designs on cool people photographs from placeit.net, a great tool for creating product visuals when you don't have a studio, camera gear, or models to wear your t-shirts.
I opened an account on the website and had advertising visuals within 2 hours.
Because my designs are simple (black design on white t-shirt), I chose happy, stylish people on plain-colored backdrops. After that, I had to develop an animated slideshow.
Because I'm a graphic designer, I chose to use Adobe Premiere to create animated Tiktok advertising.
Premiere is a fancy video editing application used for more than advertisements. Premiere is used to edit movies, not social media marketing. I wanted this experiment to be quick, so I got 3 social media ad templates from motionarray.com and threw my visuals in. All the transitions and animations were pre-made in the files, so it only took a few hours to compile. The result:
I downloaded 3 different soundtracks for the videos to determine which would convert best.
After that, I opened a Tiktok business account, uploaded my films, and inserted ad info. They went live within one hour.
The (poor) outcomes
As a European company, I couldn't deliver ads in the US. All of my advertisements' material (title, description, and call to action) was in English, hence they continued getting rejected in Europe for countries that didn't speak English. There are a lot of them:
I lost a lot of quality traffic, but I felt that if the images were engaging, people would check out the store and buy my t-shirts. I was wrong.
51,071 impressions on Day 1. 0 orders after 411 clicks
114,053 impressions on Day 2. 1.004 clicks and no orders
Day 3: 987 clicks, 103,685 impressions, and 0 orders
101,437 impressions on Day 4. 0 orders after 963 clicks
115,053 impressions on Day 5. 1,050 clicks and no purchases
125,799 impressions on day 6. 1,184 clicks, no purchases
115,547 impressions on Day 7. 1,050 clicks and no purchases
121,456 impressions on day 8. 1,083 clicks, no purchases
47,586 impressions on Day 9. 419 Clicks. No orders
My overall conversion rate for video advertisements was 0.9%. TikTok's paid ad formats all result in strong engagement rates (ads average 3% to 12% CTR to site), therefore a 1 to 2% CTR should have been doable.
My one-week experiment yielded 8,151 ad clicks but no sales. Even if 0.1% of those clicks converted, I should have made 8 sales. Even companies with horrible web marketing would get one download or trial sign-up for every 8,151 clicks. I knew that because my advertising were in English, I had no impressions in the main EU markets (France, Spain, Italy, Germany), and that this impacted my conversion potential. I still couldn't believe my numbers.
I dug into the statistics and found that Tiktok's stats didn't match my store traffic data.
Looking more closely at the numbers
My ads were approved on April 26 but didn't appear until April 27. My store dashboard showed 440 visitors but 1,004 clicks on Tiktok. This happens often while tracking campaign results since different platforms handle comparable user activities (click, view) differently. In online marketing, residual data won't always match across tools.
My data gap was too large. Even if half of the 1,004 persons who clicked closed their browser or left before the store site loaded, I would have gained 502 visitors. The significant difference between Tiktok clicks and Big Cartel store visits made me suspicious. It happened all week:
Day 1: 440 store visits and 1004 ad clicks
Day 2: 482 store visits, 987 ad clicks
3rd day: 963 hits on ads, 452 store visits
443 store visits and 1,050 ad clicks on day 4.
Day 5: 459 store visits and 1,184 ad clicks
Day 6: 430 store visits and 1,050 ad clicks
Day 7: 409 store visits and 1,031 ad clicks
Day 8: 166 store visits and 418 ad clicks
The disparity wasn't related to residual data or data processing. The disparity between visits and clicks looked regular, but I couldn't explain it.
After the campaign concluded, I discovered all my creative assets (the videos) had a 0% CTR and a $0 expenditure in a separate dashboard. Whether it's a dashboard reporting issue or a budget allocation bug, online marketers shouldn't see this.
Tiktok can present any stats they want on their dashboard, just like any other platform that runs advertisements to promote content to its users. I can't verify that 895,687 individuals saw and clicked on my ad. I invested $200 for what appears to be around 900K impressions, which is an excellent ROI. No one bought a t-shirt, even an unattractive one, out of 900K people?
Would I do it again?
Nope. Whether I didn't make sales because Tiktok inflated the dashboard numbers or because I'm horrible at producing advertising and items that sell, I’ll stick to writing content and making videos. If setting up a business and ads in a few days was all it took to make money online, everyone would do it.
Video advertisements and dropshipping aren't dead. As long as the internet exists, people will click ads and buy stuff. Converting ads and selling stuff takes a lot of work, and I want to focus on other things.
I had always wanted to try dropshipping and I’m happy I did, I just won’t stick to it because that’s not something I’m interested in getting better at.
If I want to sell t-shirts again, I'll avoid Tiktok advertisements and find another route.
You might also like

Nitin Sharma
2 years ago
Quietly Create a side business that will revolutionize everything in a year.
Quitting your job for a side gig isn't smart.
A few years ago, I would have laughed at the idea of starting a side business.
I never thought a side gig could earn more than my 9-to-5. My side gig pays more than my main job now.
You may then tell me to leave your job. But I don't want to gamble, and my side gig is important. Programming and web development help me write better because of my job.
Yes, I share work-related knowledge. Web development, web3, programming, money, investment, and side hustles are key.
Let me now show you how to make one.
Create a side business based on your profession or your interests.
I'd be direct.
Most people don't know where to start or which side business to pursue.
You can make money by taking online surveys, starting a YouTube channel, or playing web3 games, according to several blogs.
You won't make enough money and will waste time.
Nitin directs our efforts. My friend, you've worked and have talent. Profit from your talent.
Example:
College taught me web development. I soon created websites, freelanced, and made money. First year was hardest for me financially and personally.
As I worked, I became more skilled. Soon after, I got more work, wrote about web development on Medium, and started selling products.
I've built multiple income streams from web development. It wasn't easy. Web development skills got me a 9-to-5 job.
Focus on a specific skill and earn money in many ways. Most people start with something they hate or are bad at; the rest is predictable.
Result? They give up, frustrated.
Quietly focus for a year.
I started my side business in college and never told anyone. My parents didn't know what I did for fun.
The only motivation is time constraints. So I focused.
As I've said, I focused on my strengths (learned skills) and made money. Yes, I was among Medium's top 500 authors in a year and got a bonus.
How did I succeed? Since I know success takes time, I never imagined making enough money in a month. I spent a year concentrating.
I became wealthy. Now that I have multiple income sources, some businesses pay me based on my skill.
I recommend learning skills and working quietly for a year. You can do anything with this.
The hardest part will always be the beginning.
When someone says you can make more money working four hours a week. Leave that, it's bad advice.
If someone recommends a paid course to help you succeed, think twice.
The beginning is always the hardest.
I made many mistakes learning web development. When I started my technical content side gig, it was tough. I made mistakes and changed how I create content, which helped.
And it’s applicable everywhere.
Don't worry if you face problems at first. Time and effort heal all wounds.
Quitting your job to work a side job is not a good idea.
Some honest opinions.
Most online gurus encourage side businesses. It takes time to start and grow a side business.
Suppose you quit and started a side business.
After six months, what happens? Your side business won't provide enough money to survive.
Indeed. Later, you'll become demotivated and tense and look for work.
Instead, work 9-5, and start a side business. You decide. Stop watching Netflix and focus on your side business.
I know you're busy, but do it.
Next? It'll succeed or fail in six months. You can continue your side gig for another six months because you have a job and have tried it.
You'll probably make money, but you may need to change your side gig.
That’s it.
You've created a new revenue stream.
Remember.
Starting a side business, a company, or finding work is difficult. There's no free money in a competitive world. You'll only succeed with skill.
Read it again.
Focusing silently for a year can help you succeed.
I studied web development and wrote about it. First year was tough. I went viral, hit the top 500, and other firms asked me to write for them. So, my life changed.
Yours can too. One year of silence is required.
Enjoy!

Victoria Kurichenko
3 years ago
Updates From Google For Content Producers What You Should Know Is This
People-first update.
Every Google upgrade causes website owners to panic.
Some have just recovered from previous algorithm tweaks and resumed content development.
If you follow Google's Webmaster rules, you shouldn't fear its adjustments.
Everyone has a view of them. Miscommunication and confusion result.
Now, for some (hopefully) exciting news.
Google tweeted on August 18, 2022 about a fresh content update.
This change is another Google effort to remove low-quality, repetitive, and AI-generated content.
The algorithm generates and analyzes search results, not humans.
Google spends a lot to teach its algorithm what searchers want. Intent isn't always clear.
Google's content update aims to:
“… ensure people see more original, helpful content written by people, for people, in search results.”
Isn't it a noble goal?
However, what does it mean for content creators and website owners?
How can you ensure you’re creating content that will be successful after the updates roll out?
Let's first define people-first content.
What does "people-first-content" mean?
If asked, I'd say information written to answer queries and solve problems.
Like others, I read it from the term.
Content creators and marketers disagree. They need more information to follow recommendations.
Google gives explicit instructions for creating people-first content.
According to Google, if you answer yes to the following questions, you have a people-first attitude.
Do you have customers who might find your content useful if they contacted you directly?
Does your content show the breadth of your knowledge?
Do you have a niche or a focus for your website?
After reading your content, will readers learn something new to aid them in achieving their goals?
Are readers happy after reading your content?
Have you been adhering to Google's fundamental updates and product reviews?
As an SEO writer, I'm not scared.
I’ve been following these rules consciously while creating content for my website. That’s why it’s been steadily growing despite me publishing just one or two stories a month.
If you avoid AI-generated text and redundant, shallow material, your website won't suffer.
If you use unscrupulous methods to boost your website's traffic, including link buying or keyword stuffing, stop. Google is getting smarter and will find and punish your site eventually.
For those who say, “SEO is no longer working,” I dedicated the whole paragraph below.
This does not imply that SEO is obsolete.
Google:
“People-first content creators focus on creating satisfying content, while also utilizing SEO best practices to bring searchers additional value.”
The official helpful content update page lists two people-first content components:
meeting user needs
best practices for SEO
Always read official guidelines, not unsolicited suggestions.
SEO will work till search engines die.
How to use the update
Google said the changes will arrive in August 2022.
They pledged to post updates on Google's search ranking updates page.
Google also tweets this info. If you haven't followed it already, I recommend it.
Ranking adjustments could take two weeks and will affect English searches internationally initially.
Google affirmed plans to extend to other languages.
If you own a website, monitor your rankings and traffic to see if it's affected.

Vitalik
3 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
