# Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 498: 73

converges to $\dfrac{1}{1-2x}$

#### Work Step by Step

The sum of a geometric series can be found as: $S=\dfrac{a}{1-r}$ The given series shows a convergent geometric series with first term, $a=1$ and common ratio $r =2x$ $S=\dfrac{1}{1-2x}$ Hence, the given series converges to $\dfrac{1}{1-2x}$ for all $|2x| \lt 1$ or, $|x| \lt \dfrac{1}{2}$

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