Question

Find$\sum _{k=99}^{200} k^3$ . (Use Table 2.)

Short answer

Thus, the 380477799 is answer obtained using the table 2.

Step-by-step solution

Step 1:

Given:$\sum _{\mathrm{k}=99}^{200} {\mathrm{k}}^3$

We shall rewrite as a difference of sums so that the second formula of Table 2 can be used.

$\sum _{\mathrm{k}=99}^{200} {\mathrm{k}}^3$

$\begin{array}{r}=\sum _{k=1}^{200} k^3-\sum _{k=1}^{98} k^3\mid \\ =\frac{{200}^2(200+1{)}^2}{4}-\frac{{98}^2(98+1{)}^2}{4}\\ =404,010,000-23,532,201\\ =380477799\end{array}$