Prove that the sum of first n natural number squares is:
Using WolframAlpha to find the formula. WolframAlpha is a great mathematical tool.
By Mathematical Induction.
Base case : P(1)
We need to show that P(1) is true.
P(1) is true.
Assume that for some positive k, P(k) holds true, so that
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.