Chapter 12.4, Problem 11CFU

To determine

To determine whether the series is convergent or divergent.

Answer to Problem 11CFU

The series converges being a geometric series with common ratio less than $1$ .

Explanation of Solution

Given information:

  $4+3+\frac{9}{4}+\mathrm{...}$

Calculation:

  $4+3+\frac{9}{4}+\mathrm{...}$

This is an infinite geometric series with first term $a_1=4$ and common ratio $r=\frac{a_2}{a_1}=\frac{3}{4}$

Since, $\left|r\right|<1$ , the series converges.