Exactly, it could have been explicitly said that the final formula n(n+1)/2 is the formula for sum from 1 to n. It's well known but turning it back into the explicit sum is more impactful
The idea is that the squares have a side length of some integer a, so they have an area of a^2, but because you have a total of a of these squares, the total area for each integer is a * a^2 which is a^3.
Brilliant visualisation
one of the best visual proofs ive seen
And it can also be represented as 1³+2³+....n³= (1+2+3...+n)² as i know
Exactly, it could have been explicitly said that the final formula n(n+1)/2 is the formula for sum from 1 to n. It's well known but turning it back into the explicit sum is more impactful
nichomachus theorem
oooh look at you
See my short from around New Years's :)
Amazing.
Do you come up with these proofs by yourself or its sourced?
They are pretty much all sourced. Every description has a link to the original.
1^3+2^3+.....+n^3=(1+2+....+n)^2
If it is 1^3+.......+ n^3, then why did you start with squares, wouldn't you have to use cubes?
The idea is that the squares have a side length of some integer a, so they have an area of a^2, but because you have a total of a of these squares, the total area for each integer is a * a^2 which is a^3.
Imagine the n layers of an n by n by n cube (each being an n by n square) laid out side by side.
Good job
Triangle(n)^2
Why 1+2+3+4+…+n=n(n+1):2?
Check my channel. I have a dozen proofs in one wide form video of that fact.
@ ok
🤯
Why not simply ( 1+2+3...+n)²