Chapter 13.4, Problem 60STP

To determine

To find:The sum of each infinite series, if it exists.

Answer to Problem 60STP

Sum of given infinite series $=256$

Explanation of Solution

Given information:

  $64+48+36+\mathrm{....}$

This represents the below series

  $64+48+36+\mathrm{....}$

This is a Geometric series.

Sum of infinite terms of Geometric series $S=\frac{a}{1-r}$

From above series

We can say that

  $a=64$

Common ratio $=r=\frac{48}{64}=\frac{36}{48}=0.75$

Since $\left|0.75\right|<1$ , the series is Convergent.

So, sum of infinite series will exist.

On substituting values

We get

  $\begin{array}{l}S=\frac{a}{1-r}\\ \Rightarrow S=\frac{64}{1-0.75}\\ \Rightarrow S=\frac{64}{0.25}\\ \Rightarrow S=256\end{array}$

Therefore,

Sum of given infinite series $=256$