Answer
$\displaystyle \frac{1}{2}+2+\frac{9}{2}+8+\frac{25}{2}+18+\frac{49}{2}+\cdots+\frac{n^{2}}{2}$
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:
$\displaystyle \sum_{k=1}^{n}\frac{k^{2}}{2}=\frac{(1)^{2}}{2}+\frac{(2)^{2}}{2}+\frac{(3)^{2}}{2}+...+\frac{(n)^{2}}{2}$
$=\displaystyle \frac{1}{2}+2+\frac{9}{2}+8+\frac{25}{2}+18+\frac{49}{2}+\cdots+\frac{n^{2}}{2}$
