Chapter 2.4, Problem 39E

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

TABLE 2 Some Useful Summation Formulae.
Sum	Closed Form
$\begin{array}{l}{\displaystyle \underset{k=0}{\overset{n}{\sum }}a{r}^k\left(r\ne 0\right)}\\ {\displaystyle \underset{k=1}{\overset{n}{\sum }}k}\\ {\displaystyle \underset{k=1}{\overset{n}{\sum }}{k}^2}\\ {\displaystyle \underset{k=1}{\overset{n}{\sum }}{k}^3}\\ {\displaystyle \underset{k=0}{\overset{\infty }{\sum }}{x}^k,\left|x\right|<1}\\ {\displaystyle \underset{k=1}{\overset{\infty }{\sum }}k{x}^{k-1},\left|x\right|<1}\end{array}$	$\begin{array}{l}\frac{a{r}^{n+1}-a}{r-1},r\ne 1\\ \frac{n\left(n+1\right)}{2}\\ \frac{n\left(n+1\right)\left(2n+1\right)}{2}\\ \frac{n^2{\left(n+1\right)}^2}{4}\\ \frac{1}{1-x}\\ \frac{1}{{\left(1-x\right)}^2}\end{array}$