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

Prove by Mathematical Induction that the assertion,

n

∑ r^2 = n/6 (n+1)(2n+1)

r=1

holds for every natural number n.

2. Relevant 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.

3. 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?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Help with mathematical assertions for natural numbers

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