The sum of the squares of the first n natural numbers
Submitted by Isoscel on Tue, 11/27/2007 - 21:56.
What is the sum of the squares of the first n natural numbers?
The answer is:
![]() |
Here is a calculator that calculates this function for you:
n:
:
Proof:
We write the above identity for k from 1 to n:
...
We add this n identities and we get:
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |