Question

Find$\sum _{k=100}^{200} {100}^k$ . (Use Table 2.)

Short answer

Thus, the is answer obtained by using Table 2.

Step-by-step solution

Step 1:

Given :$\sum _{k=100}^{200} k$

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

$\begin{array}{r}=\sum _{k=1}^{200} k-\sum _{k=1}^{99} k\\ =\frac{200(200+1)}{2}-\frac{99(99+1)}{2}\\ =20100-4950\\ =15150\end{array}$