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## Homework Statement

Consider ##\sum\limits_{n=0}^{\infty} \frac{n+1}{(2n)!}(x+1)^{2n+1}##. Find the interval of convergence and sum of the power series.

## Homework Equations

## The Attempt at a Solution

According to the textbook: given the power series ##\sum a_n(x-c)^n## the radius of convergence ##R:=\frac{1}{\lim\limits_{n\to\infty}\frac{a_{n+1}}{a_n}}##. It doesn't say anything about a series ##\sum a_n(x-c)^{f(n)}## where ##f(n)= 2n +1##, for example. Can I use the said formula to calculate ##R## in this case? ##a_n =\frac{n+1}{(2n)!}## If so then:

[tex]R:=\frac{1}{\lim\limits_{n\to\infty} \frac{(n+2)(2n)!}{(2n+2)!(n+1)}} = \frac{1}{0}?[/tex]