Question

Find the radius of convergence and interval of convergence of the following series.

Answer 1

\[\sum_{n=0}^{\infty} (-1)^n \frac{ (x-4)^n }{ 4n+1 }\]

Answer 2

Set up the ratio test, but stuck from there
\lim_{n \rightarrow \infty}|\frac{ (x-4)^n+1 }{ 4(n+1)+1 }*\frac{ 4n+1 }{ (x-4)^n }|\]

Answer 3

\[\lim_{n \rightarrow \infty}|\frac{ (x-4)^n+1 }{ 4(n+1)+1 }*\frac{ 4n+1 }{ (x-4)^n }|\]\]

Answer 4

Found a similar example and got it - nevermind!