Having trouble with when to apply the ratio test for power series and when to apply the ratio test for real numbers.
For example, find radius of convergence of these....
$\sum_{n=0}^{\infty}(-1)^n (x+3)^n$
For this I would use ratio test for power series and get radius of convergence = 1, fine.
but for
$\sum_{n=0}^{\infty}n!(n+1)!(x+1)^{2n}$
Why do we need to use the ratio test for real numbers, and define for a fixed $x$? and why can't we use the ratio test for power series?
Is it because the $(x+1)^{2n}$ part is $2n$ and not $n$?