Consider the series ${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n(2x+3{)}^n$

$(a)$ Find the series' radius and interval $of$ convergence.

$(b)$ For what values $ofx$ does the series converge $absolutely?$

$(c)$ For what values $ofx$ does the series converge conditionally?

$(a)$ The interval $of$ convergence $is$

$|.(Simplify$ your answer. Type your answer $in$ interval notation.$)$