Answer
$4+9+16+25+36+\cdots+(n+1)^{2}$
Work Step by Step
There are n terms, as the index k changes from 1 to n.
The index k dictates how the terms are formed:
$\displaystyle \sum_{k=1}^{n}(k+1)^{2}=(1+1)^{2}+(2+1)^{2}+(3+1)^{2}+...+(n+1)^{2}$
$=4+9+16+25+36+\cdots+(n+1)^{2}$