# For what values of x does this series converge

1. Apr 1, 2007

### Gauss177

1. The problem statement, all variables and given/known data
Series is:

(ln x)^n, n goes from 1 to infinity

2. Relevant equations

3. The attempt at a solution
For other problems I've seen the ratio test used to find the radius of convergence, but I don't think this can work here. What other things can I do to find where this converges?

2. Apr 1, 2007

### mattmns

For what values of x does the series:

$$\sum_{n=1}^{\infty}x^n$$

converge?

Last edited: Apr 1, 2007
3. Apr 2, 2007

### HallsofIvy

Why wouldn't the ratio test work here? The ratio test, remember, works for every infinite series, not just power series.
$$\frac{(ln x)^n}{(ln x)^{n+1}}= \frac{1}{ln x}$$
In order that the series converge, that fraction must be less than 1.

(And, of course, that gives the same answer as mattmns' solution.)

Last edited by a moderator: Apr 2, 2007