Answer
series diverges
Work Step by Step
RECALL:
(1)
In the infinite geometric series:
$$\sum_{k=1}^{\infty}c \cdot r^{n-1}$$
$r$ is the common ratio.
(2)
A geometric series converges if $|r| \lt 1$. The sum of a convergent infinite geometric series is given by the formula:
$S_{\infty}=\dfrac{a_1}{1-r}$
where
$r$ = common ratio
$a_1$ = first term
$\bf\text{Solve for r}:$
Note that when a geometric series is summation notation, the expression being raised to a power is the common ratio.
Thus, the common ratio of the given series is $\dfrac{3}{2}$.
Since $|\frac{3}{2}|=\frac{3}{2} \gt 1$, the series diverges.
