Answer
The Ratio Test or the Root Test
Work Step by Step
In order to determine the radius of convergence of a power series we can use either the Ratio Test, or the Root Test.
Example: 1) For the series $\sum_{k=0}^{\infty} \dfrac{x^k}{(k+1)!}$ we should use the Ratio Test.
2) For the series $\sum_{k=0}^{\infty}\dfrac{(x+1)^k}{5^k}$ we should use the Root Test.
