Question

Find the radius of \[\sum_{n=1}^\infty \dfrac{(-3)^n}{n^3}x^n\]
Please help

Answer 1

Have you tried the ratio test?

Answer 2

\[\lim_{n\to\infty}\left|\frac{\dfrac{(-3)^{n+1}x^{n+1}}{(n+1)^3}}{\dfrac{(-3)^nx^n}{n^3}}\right|=|x|\lim_{n\to\infty}\frac{3n^3}{(n+1)^3}\]
The limit has to be less than \(1\) in order for the series to converge.

Answer 3

Thanks for the help.:)

Answer 4

yw