Answer
$\sum_{k=99}^{200} k^{3}$
Rewrite as a difference of sums
$=\sum_{k=1}^{200} k^{3}-\sum_{k=1}^{98} k^{3}$
$=\frac{200^{2}(200+1)^{2}}{4}-\frac{98^{2}(98+1)^{2}}{4}$
$=404,010,000-23,532,201$
$=380477799$
Work Step by Step
$\sum_{k=99}^{200} k^{3}$
Rewrite as a difference of sums
$=\sum_{k=1}^{200} k^{3}-\sum_{k=1}^{98} k^{3}$
$=\frac{200^{2}(200+1)^{2}}{4}-\frac{98^{2}(98+1)^{2}}{4}$
$=404,010,000-23,532,201$
$=380477799$
