Answer
The series diverges.
Work Step by Step
The common ratio of a geometric sequence is equal to the quotient of any term and the term before it:
$ \ r = \dfrac{a_n}{a_{n-1}}$ or, $r=\dfrac{a_2}{a_1}$
The sum of a convergent infinite geometric series is given by the formula:
$S_{\infty}=\dfrac{a_1}{1-r}$ and a geometric series converges if $|r| \lt 1$.
where $r \ =common \ ratio \ =\dfrac{3}{2}$
Since $r=|\dfrac{3}{2}| \gt 1$, the infinite geometric series diverges.
