Question: Find the open interval of convergence and test the end points for absolute and conditional convergence.

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

(b) \(\sum\limits_{n=1}^{\infty }{\frac{{{2}^{n}}{{x}^{n}}}{\sqrt{n}}}\)