Sum and product problem

Question

How can I find the result of:

$\sum\limits_{i=1}^{n}\prod\limits_{j=1}^{2} ij$

I know that $\prod\limits_{j=1}^{2} ij = 2i^2$, so I should simply do the summation as $\sum\limits_{i=1}^n2i^2$?

Answer 1

This should be easy:

$$ \sum_{i=1}^n 2i^2 = 2 \sum_{i=1}^n i^2 = 2 \frac{n(n+1)(2n+1)}{6} = \frac{n(n+1)(2n+1)}{3}$$