Answer
$$
18,755
$$
Work Step by Step
Write sum:
$\sum_{k=0}^{29}(-k+30)(-k+50)$
Rewrite sum:
$\sum_{k=1}^{30}(-k+31)(-k+51)$
Expand brackets:
$\sum_{k=1}^{30}\left(1581-82 k+k^{2}\right)$
$-82 \cdot \frac{31\cdot 30}{2}+30 \cdot 1581 +\frac{31 \cdot 61 \cdot 30}{6}$
Write in closed form:
18,755
