# Sum of n natural number squares

Prove that the sum of first n natural number squares is:

i.e

Using WolframAlpha to find the formula. WolframAlpha is a great mathematical tool.

### Proof:

By Mathematical Induction.

Base case : P(1)

We need to show that P(1) is true.

1=1

P(1) is true.

Assume that for some positive k, P(k) holds true, so that

P(k)

We need to show that P(k + 1) holds true.

We have assumed that P(k) is true. Replacing for k terms we get:

Taking (k+1) common we get :

Take hints in the factorization, we need to prove and eventually get (k+1) in terms of k.

expand and rearrange the 2nd term:

Taking k+2 common

Hence P(k + 1) holds true, when P(k) is true, so P(n) is true for all finite natural numbers n.