1. ## Power Series

I need to find the interval on convergence of the given power series

I am trying to do summation of nx^x
I am using s(n+1)/s(n) to solve the problem, but am having trouble getting an answer. Thanks for the help.

2. Originally Posted by davecs77
I need to find the interval on convergence of the given power series

I am trying to do summation of nx^x
I am using s(n+1)/s(n) to solve the problem, but am having trouble getting an answer. Thanks for the help.
We wish to find the radius of convergence for $\sum_{n = 1}^{ \infty} nx^n$

We will proceed by the Ratio test (since that's what you wanted, I'd probably do the root test here).

Let $s_n = nx^n$

by the Ratio test, we have convergence if $\lim_{n \to \infty} \left| \frac {s_{n + 1}}{s_n}\right| < 1$

Now, $\lim_{n \to \infty} \left| \frac {(n + 1)x^{n + 1}}{nx^n} \right| = \lim_{n \to \infty} \left| \frac {n + 1}{n} \cdot x \right| = |x|$

Thus we have convergence if $|x| < 1$

so our radius of convergence is 1

3. Originally Posted by Jhevon
i believe it should be x^n, am i right?

oops I messed up..actually it should be
summation of nx^(n)

4. Originally Posted by davecs77
oops I messed up..actually it should be
summation of nx^(n)
yes, i realize that, i already gave you the required solution