## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Converges; $\dfrac{4}{3}$
An infinite geometric series is said to converge if and only if $|r|\lt1$, and the sum can be expressed as: $a_n=\dfrac{a_1}{1-r}$ where $a_1=\ First \ Term$ and $r$ is the common ratio of the quotient of two consecutive terms. Since, $a_1=2$ and $r=\dfrac{a_2}{a_1}=\dfrac{-1}{2}$ Because $r= |\dfrac{-1}{2}| =\dfrac{1}{2} \lt1$ Therefore, the series converges and its sum is equal to: $a_n=\dfrac{2}{1-(\dfrac{-1}{2})}=\dfrac{4}{3}$