Answer
Diverges
Work Step by Step
An infinite geometric series is said to converge if and only if $|r|\lt1$, and diverges when $|r| \gt 1$.
The sum of a geometric series 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{3/4}{1/2}=\dfrac{3}{2} $
Because $r= |\dfrac{3}{2}| =\dfrac{3}{2} \gt 1$
Therefore, the series diverges.
