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Sorry for no formatting, i don't know how it works here.

The question is:

Using induction, for n in the natural numbers, demonstrate sum of i^2 from i=1 to n is equal to (n(n+1)(2n+1))/6.

I got to the point of telescoping the values to:

a_{n} - a_{1} = 3 + 5 + ... + (2n-1)

a_{n} = 3 + 5 + ... + 2n

And had a few other side parts like:

a_{n} - a_{n-1} = n^2

a_{n} - a_{n-1} = 2n-1

But I got nowhere else with it.

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    [edit] the question to use mathjax for formatting: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Ethan Bolker Nov 01 '24 at 01:15

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