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## Homework Statement

Prove by Mathematical Induction that the assertion,

n

∑ r^2 = n/6 (n+1)(2n+1)

r=1

holds for every natural number n.

## Homework Equations

Ok, so basically, how do you solve this question? I have got to the Induction step but I'm not sure how to do it.

## The Attempt at a Solution

I've replaced n with k so I have,

1^2 + 2^2 + 3^2 + ... k^2 = k/6 (k+1)(2k+1)

Then I've added the (k+1)th term to each side to I have,

1^2 + 2^2 + 3^2 + ... k^2 + (k+1)^2 = k/6 (k+1)(2k+1) + (k+1)^2

So where do I go from here?