## Calculus 8th Edition

$n^{2}+(n+1)^{2}+(n+2)^{2}+(n+3)^{2}$
We expand the sigma notation by writing $j^{2}$ as $j$ increases from n to n+3: $\displaystyle \sum_{j=n}^{n+3}j^{2}=n^{2}+(n+1)^{2}+(n+2)^{2}+(n+3)^{2}$ (We could expand this, but this is not required of the problem.)