Proof Of The Sum Of Squares Formula

Here is a proof, using induction, that the sum of squares up to N² is N(N + 1)(2N + 1) / 6 for any natural number N:

• It is true for N = 0 and N = 1.
• (N + 1)((N + 1) + 1)(2(N + 1) + 1) / 6 - N(N + 1)(2N + 1) / 6 = (N + 1)²
• Therefore, the sum of squares up to N² is N(N + 1)(2N + 1) / 6 for any natural number N.
• QED