When I apply the root test to power series I know that
So if I get $1$ as the result of the limit the radius of convergence of the power series is $R=1$?
Same question also for the ratio test.
I'm confused because when I study the behaviour of numerical series with these criteria and I get 1 as a result it means that they are not applicable.
The prove of the ratio test given on Wikipedia though seems to me clear in indicating that in the power series case $1$ is not a problematic result.