# Chapter 12 Sequences and Series - Chapter Review - Page 842: 24

$8$

#### Work Step by Step

An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term. Here $r=\frac{5}{8},a_1=3$ Thus $|\frac{5}{8}|\lt1$, hence the sum exists. Hence the sum: $\dfrac{3}{1-\frac{5}{8}}=8$

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