Chapter 13.4, Problem 62STP

To determine

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

Answer to Problem 62STP

Sum of infinite series does not exist

Explanation of Solution

Given information:

  ${\displaystyle \sum _{n=1}^{\infty }0.5{\left(1.1\right)}^n}$

This represents the below series

  ${\displaystyle \sum _{n=1}^{\infty }0.5{\left(1.1\right)}^n}$

This is a Geometric series.

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

From above series

We can say that

Common ratio $=r=1.1$

Since $\left|1.1\right|>1$ , the series is Divergent.

So, sum of infinite series does not exist.