Question

Find the interval of convergence

Answer 1

I need to find the interval of convergence of this power series
\[\sum_{n=0}^{∞}(-1)^n \frac{ n(x+1)^n }{ 4^n(n+2) } \]
Can I just use the normal method \[\lim_{n \rightarrow ∞}\left| \frac{ a_{n+1} }{ a_n } \right|\]
Or do
\[(-1)^n\]
have a infect on the result?

Answer 2

you pull out the non "n" parts into an absolute value; so the -1 is really moot