@mikoliism
Combinatorial proofs are so cool, I wish they were touched on more in discrete math classes
@BernardGreenberg
Why is this better than the straighforward demonstration of the sum of any geometic series?
@prakharsingh4763
My brain left the skull
@MrOkazak1
This can be generalized to (X-1)(X^0+X^1+X^2....+X^(N-1))=X^N. Most obvious in Base 2 and Base 10.
@BlackbodyEconomics
This has quickly become one of my favorite math chans of all time. This is a fascinating example :) Thank you!
@mrbutish
Nice finally a good explanation to creating fractals manually
@Vobacoach
Damn I am SO amazed by your grafik proofs and explanations!!! Huge Respects to you!
@mo2cubing
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: (X-1)*(x^1+x^2+...+x^(n-2)+x^(n-1))+1=x^n
@noahgilbertson7530
I love this identity, because everyone secretly knows it from when they learnt how to add big numbers together
@anandmaurya8479
This is proof that sometimes things are better if not visualised
@jacksonstenger
Nice one, an interesting mix of combinatorial and geometric
@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 10^4.
@حسينالقطري-ب8ص
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😊
@prakashlakhapate1598
This is true for any no 5(1+6)+1 = 36=6^2 Dhanyavad!!! Prakash Lakhapate
@Supersmart-g8k
This is fascinating glad I can understand math Mathematics is beautiful
@happyvirus6590
Damn. Math really looks like this reality's magic system.
@MydniteMoonrabbit
No one pointing out that it looks like a snowflake
@greenGuy4969
Fun fact this works with every number but instead of multiplying by 6 you multiply by n-1
@Mari0Kid1234
It’s a beautiful fractal aswell
@jakobr_