Chapter 12.5, Problem 19E

To determine

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

Answer to Problem 19E

Sum of the given series is $496$ .

Explanation of Solution

Given information:

Given series is,

  ${\displaystyle \sum _{j=4}^8{2}^j}$

  $\begin{array}{c}{\displaystyle \sum _{j=4}^8{2}^j}=\left(2^4\right)+\left(2^5\right)+\left(2^6\right)+\left(2^7\right)+\left(2^8\right)\\ =16+32+64+128+256\\ =496\end{array}$

Hence the sum of the given series is $496$ .