Sunday, 26 August 2018

sequences and series - How to derive the formula for the sum of the first $n$ perfect squares?

How do you derive the formula for the sum of the series when $S_n = \sum_{j=1}^n j^2$?



The relationship $(n, S_n)$ can be determined by a polynomial in $n$. You are supposed to use finite differences to determine the degree and then use a calculator to derive the function. But how?

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