Geometric sum of powers of 7

This is a short, animated visual proof demonstrating the finite geometric sum formula for any integer n with n greater than 3 (explicitly showing the case n=7 with k=3). This series (and its infinite analog when x less than 1) is important for many results in calculus, discrete mathematics, and combinatorics.

Thanks!

#manim​ #math #geometricsums #series​ #calculus #mtbos​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #finitesums #finiteseries #geometric #mathshorts​ #mathvideo​

To learn more about animating with manim, check out:

[jakobr_]

As Matt Parker recently pointed out, this is obvious when written in base 7

[BernardGreenberg]

Why is this better than the straighforward demonstration of the sum of any geometic series?

[mrbutish]

Nice finally a good explanation to creating fractals manually

[BlackbodyEconomics]

This has quickly become one of my favorite math chans of all time. This is a fascinating example :) Thank you!

[Vobacoach]

Damn I am SO amazed by your grafik proofs and explanations!!! Huge Respects to you!

[MrOkazak]

This can be generalized to Most obvious in Base 2 and Base 10.

[jacksonstenger]

Nice one, an interesting mix of combinatorial and geometric

[mocubing]

The formula also works for other numbers. For example, if you add all the powers of 2 up until you get to 2^(n-1) and multiply that by 1 then add 1, you get 2^n. I guess the formula could therefore be, where x represents the base number, and n represents the power:

[حسينالقطري-بص]

Nice video as usual ❤

I am still waiting for a special video, explaining how you make these animations. It will be useful for many people. Please do it😊

[Supersmart-gk]

This is fascinating glad I can understand math
Mathematics is beautiful

[anandmaurya]

This is proof that sometimes things are better if not visualised

[happyvirus]

Damn. Math really looks like this reality's magic system.

[MydniteTheSpaceWolpertinger]

No one pointing out that it looks like a snowflake

[RetroGDGamer]

If you didn't underatand it, here's an easier way:
1+10+100+1000=1111, right?
And multiply that by 9 and you have 9999. You still with me?
Add 1 and boom, 10000, which is the same as 10^5.

[zacharywaldron]

Here I was expecting a different fractal being formed by taking the circle and drawing 6 more inside the circle and repeat recursively. But this would create another form of a snowflake fractal.

[greenGuy]

Fun fact this works with every number but instead of multiplying by 6 you multiply by n-1

[WhoIsMrKemp]

No wonder 7 has always been my favorite number

[SotirakisPeklivanas]

This can be done for any shape. Does this mean one formula fits all?

[anadiacostadeoliveira]

Have you seen the Koch Snowflake? This one is similar to the Koch Snowflake fractal 😮😊

[emjizone]

Why 7? What is the point of not deponstrating it for any integer superior to 0?