Answer
Converges; $8$
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, $a_1=4$ and $r=\dfrac{a_2}{a_1}=\dfrac{1}{2} $
Because $r= |\dfrac{1}{2}| \lt1$
Therefore, the series converges and its sum is equal to: $a_n=\dfrac{4}{1-\dfrac{1}{2}}=8$
