How to represent this partial sum? I'm trying to find a way to represent $\sum_{n=1}^\infty n^2$ as a partial sum. I know that every term in this series can be represented, for example when $n=5$, as $5^2+4^2+3^2+2^2+1^2$. I know that $1+2+3+4...$ can be represented as $\frac{n(n+1)}{2}$ but I can't figure out how to add the squared terms to each number.

What you're looking for is
$$\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}{6}$$
