Answer
The series is convergent.
$\sum_{n=1}^\infty\frac{6}{(-3)^n}=-1.5$
Work Step by Step
The graph of the sequence of terms and the sequence of partial sums is given below.
From the graph, the sequence of partial sums $S_n$ approaches $-1.5$ as $n$ becomes larger, so that the series is convergent.
The series $\sum_{n=1}^\infty\frac{6}{(-3)^n}$ is an infinite geometric series with the first term $a_1=-2$ and the common ratio $r=-\frac{1}{3}$.
Find the sum of the series:
$\sum_{n=1}^\infty\frac{6}{(-3)^n}=\frac{a_1}{1-r}=\frac{-2}{1-(-\frac{1}{3})}=\frac{-2}{4/3}=-1.5$
