Answer
$\displaystyle \sum_{k=1}^{4}\left[1-\left(\frac{k}{4}\right)^{2}\right]$
Work Step by Step
There are n terms in the sum (we don't know n yet)
Each term has the same form:
$[1-(\displaystyle \frac{k}{4})^{2}]$,
with the 1 and 4 appearing in all the terms unchanged,
the numerator k assumes values 1,2,3,4
So n=4 terms, and we use k for indexing:
$\displaystyle \sum_{k=1}^{4}\left[1-\left(\frac{k}{4}\right)^{2}\right]$
