Calculus 101: Geometric Series

William Spaniel explores the proof for geometric series, which are necessary for games that model time in the interaction. However, this video is suitable to students of calculus exclusively.

The Burning Question:
In the movie I.Q., Meg Ryan is standing 2 feet away from Tim Robbins. She tells him that he can walk half the distance to her. Then, he can walk half the remaining distance. Then he can walk half the remaining distance again. And so forth. If he ever reaches her, he may kiss her.

Will Tim Robbins ever kiss Meg Ryan? The answer may surprise you,.

[Gametheory]

@1337SuperNewb He will if he can take the steps fast enough--think of a bouncy ball falling to the ground.

Is this possible? Well, have you seen Shawshank Redemption? If Tim Robbins can do that, he can do anything.

[Gametheory]

@A2THEANDREW23 I don't do physics, but I think so. Is this similar to why a bouncy ball eventually stops bouncing?

[cajunxxsunrise]

William, thank you so much for providing this excellent resource. My professor is great, but decided not to provide a textbook for the course, and this is an excellent review to his material.

[brainofjikir]

@A2THEANDREW23 No, if you model an oscillating system (like a spring and block) it has to do with the exponential function and taking it over some time constant and taking that to infinity. But, the formula has a negative multiplied by that, so it really dies off exponentially, not geometrically.

[Gametheory]

It's more strategic and less about intuition. We ultimately want to solve for S but there are a whole bunch of terms making things inconvenient. Creating the second line and subtracting it from the first is just a tricky way of removing a whole bunch of terms that would otherwise muck things up.

[unminified]

I still don't really understand the intuition behind why you subtracted @ 3:05. Could you explain why we do that there?

[ATHEANDREW]

so could one use this same "system" of solving the equation in order to factor in a coefficient of friction in a physical problem ?

[Kriegter]

Well now this explains war maths. Now I need to know war maths.

[ATHEANDREW]

@JimBobJenkins This video helped me integrate my limited CALC. knowledge into my algebra based physics class, you can use this technique for a plethora of problems; and yes the bouncing ball is one.

[FataKu]

In practice however, if you're standing less than an 8th of an inch away from a person, you've probably reached them by then. If not, you may want to exert sufficient pressure to atomically fuse to that person. I'm not going to lose simply because of the distance between a neutron and an electron!

[redarrowhead]

infinite is a theoretical value. It can never be applied in a real life setting, since nothing lasts forever. Although Robins would, theoretically, reach the girl, he would have to walk forever.

[ThePatrickFamilyBand]

That's why I thought that he shouldn't play the game, but apparently we can reach infinity? ;)

[ThePatrickFamilyBand]

Hmmm ... I never thought of that, lol.

[Sedruk]

the idea is you can calculate the finite in infinity. so if he kept stepping closer infinitly he would reach her in "x" amount of steps. It seems like a pointless concept to me. Nevertheless it is pretty damn cool.

[SuperNewb]

Wouldn't Tim Robbins never reach the girl because it is impossible to reach infinity? I mean infinity isn't a number but an idea that we can simply get closer to. Given any number of steps he takes towards her, he would still have to take more steps in order to reach her.

[cigarscool]

that was awesome and very helpful, thank you so much, never thought of kissing a chick during a math problem

[philnoll]

If you're playing this game and you haven't won yet, don't get discouraged. I'm sure you'll make it one of these days.

[neelaakaasham]

i dont understand how you conclude he can cover the distance. The limit you take only gives an approximation, and not an absolute value. You can reach infinitesimally close to the full distance but not quite make it. Clearly the problem states you move only half distance each time, and therefore would take infinite number of steps to cover the distance. And you cannot walk infinite number of steps. So i think your conclusion is wrong.