Chapter 13.4, Problem 61STP

To determine

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

Answer to Problem 61STP

Sum of infinite series does not exist

Explanation of Solution

Given information:

  $27+36+48+\mathrm{....}$

This represents the below series

  $27+36+48+\mathrm{....}$

This is a Geometric series.

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

From above series

We can say that

  $a=27$

Common ratio $=r=\frac{36}{27}=\frac{48}{36}=\frac{4}{3}$

Since $\left|\frac{4}{3}\right|>1$ , the series is Divergent.

So, sum of infinite series does not exist.