Chapter 12.5, Problem 21E

To determine

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

Answer to Problem 21E

Sum of the given series is $\frac{171}{2}$ .

Explanation of Solution

Given information:

  ${\displaystyle \sum _{r=1}^3\left(\frac{1}{2}+4^r\right)}$

  $\begin{array}{c}{\displaystyle \sum _{r=1}^3\left(\frac{1}{2}+4^r\right)}=\left(\frac{1}{2}+4^1\right)+\left(\frac{1}{2}+4^2\right)+\left(\frac{1}{2}+4^3\right)\\ =4\frac{1}{2}+16\frac{1}{2}+64\frac{1}{2}\\ =\frac{171}{2}\end{array}$

Hence the sum of the given series is $\frac{171}{2}$ .