# Thread: convergent for the values ​​of x

1. ## convergent for the values ​​of x

Hi,

The following series is convergent for the values ​​of x?

$\sum_{n=o}^{\infty }\frac{n}{x^n}$

thanks

2. ## Re: convergent for the values ​​of x

Originally Posted by vernal
Hi,

The following series is convergent for the values ​​of x?

$\sum_{n=o}^{\infty }\frac{n}{x^n}$

thanks
The ratio test states that the series will be convergent where \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| < 1 \end{align*}, divergent where \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| > 1 \end{align*}, and inconclusive where \displaystyle \begin{align*} \left|\frac{a_{n+1}}{a_n}\right| = 1 \end{align*}. So a good place to start would be to evaluate where this ratio is less than 1.

3. ## Re: convergent for the values ​​of x

Not necessary.

4. ## Re: convergent for the values ​​of x

Originally Posted by HallsofIvy
Not necessary.
Seeing as your post was as useless as it was insulting, why not explain a quicker method for the OP?