Chapter 11.5, Problem 13WE

To determine

To calculate:

Sum of given geometric series.

Answer to Problem 13WE

Sum of given geometric series is $255$ .

Explanation of Solution

Give information:

  $n=8,r=2,t_1=1$

Calculation:

Given series is,

  $n=8,r=2,t_1=1$

To find sum of geometric series,

  $S_n=\frac{a_1{\left(1-r\right)}^n}{1-r}$

Where,

  $a_1=$ First term,

  $r=$ Common ratio.

After substituting the values in above equation,

  $\begin{array}{l}{S}_n=\frac{a_1\left(1-r^n\right)}{1-r}\\ S_n=\frac{1\left(1-2^8\right)}{1-2}\\ S_n=\frac{\left(1-256\right)}{-1}\\ S_n=255\end{array}$

Therefore, Sum of given geometric series is $255$ .