I'm stuck with my homework:
Find both the radius and interval of convergence for the given series. Also, determine the values of $x$ for which the series converges absolutely and those for which the series converges conditionally.
(a) $\displaystyle\sum_{k=1}^{\infty}k(x-2)^k$
(b) $\displaystyle\sum_{k=1}^{\infty}\frac{1}{k}\left(\frac{x}{2}\right)^k$
(c) $\displaystyle\sum_{k=1}^{\infty}k\left(-\frac{1}{3}\right)^k(x-2)^k$
(d) $\displaystyle\sum_{k=1}^{\infty}\frac{2^kk!}{k^k}x^k$
(e) $\displaystyle\sum_{k=1}^{\infty}\frac{k}{3^{2k-1}}(x-1)^{2k}$