Chapter 12.5, Problem 18E

To determine

To write given expression in expanded form and them find its sum.

Answer to Problem 18E

Sum of the given series is $\frac{37}{3}$ .

Explanation of Solution

Given information:

Given series is,

  ${\displaystyle \sum _{n=5}^8\left(\frac{n}{n-4}\right)}$

  $\begin{array}{c}{\displaystyle \sum _{n=5}^8\left(\frac{n}{n-4}\right)}=\left(\frac{5}{5-4}\right)+\left(\frac{6}{6-4}\right)+\left(\frac{7}{7-4}\right)+\left(\frac{8}{8-4}\right)\\ =5+3+\frac{7}{3}+2\\ =\frac{37}{3}\end{array}$

Hence the sum of the given series is $\frac{37}{3}$ .