Consider the power series

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{(2x+3{)}^{2n+1}}{n!}$

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

$($b$)$ Identify the values of x for which the above series converges $($i$)$ absolutely$,($ii$)$ conditionally. Give solution Of this question