Suppose $\sum_{k=0}^{\infty} {a_k}{x^k}$ is a power series and $$\lim_{k\rightarrow\infty}|a_k|^\dfrac{1}{k}$$=L>0 converges
Prove that $\sum_{k=0}^{\infty} \dfrac{a_k}{k+1}{x^k}$ Has a radius of convergence R=$\dfrac{1}{L}$.
I have no idea where to start, all of the examples I have seen use the ratio test to find the radius of convergence, (usually something like $\sum_{k=0}^{\infty} \dfrac{x^n}{n!}$ or $\sum_{k=0}^{\infty} \dfrac{x^2n}{n(2n)}$ I can find the radius of convergence for these). But I haven't seen any examples with ${a_k}$ in the series. Any help would be greatly appreciated. Thank you,