# For what values of x does this series converge

## Homework Statement

Series is:

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

## 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?

For what values of x does the series:

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

converge?

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HallsofIvy
Homework Helper

## Homework Statement

Series is:

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

## 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?

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.)

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