I'm asked to find the radius of convergence of a bunch of different series.
In the solutions, a mixture of the root and ratio tests are used. But, it is unclear to me which to use when.
For example, one of the series:
$\sum_{n=1}^{\infty} \frac{2^n}{n^2} z^n$, the official solutions use the root test, but I get the same answer if I use the ratio test.
Since the root test implies the ratio test, should I in general only use the root test?