(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

prove:

0^2 + 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6

2. Relevant equations

3. The attempt at a solution

I'm confused on how to prove this by induction. I'm not exactly sure what the goal of the rearrangement is after substituting (n+1). Any help is much appreciated!

base case: n = 0

0^2 = 0(0+1)(2*0+1)/6

induction step:

(0^2+1^2+2^2+...+n^2) + (n+1)^2 = (n+1)((n+1)+1)(2(n+1)+1)/6

n(n+1)(2n+1)/6 + (n+1)^2

(n+1)[n(2n+1)/6 + (n+1)]

...here is where I'm lost, I'm not sure what I'm trying to manipulate it to look like....

Thanks!

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# Help with simple proof by mathematical induction

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