Question: Find the radius of convergence and the interval of convergence for each of the series listed below

a- \(\sum\limits_{k=1}^{\infty }{\frac{{{5}^{k}}{{x}^{k}}}{{{k}^{2}}}}\)

b- \(\sum\limits_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n}}{{x}^{2n}}}{\left( 2n \right)!}}\)

c- \(\sum\limits_{k=1}^{\infty }{\frac{\ln k{{\left( x-1 \right)}^{k}}}{k}}\)