For what values of x does this series converge

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  • #1
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Homework Statement


Series is:

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

Homework Equations




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?
 

Answers and Replies

  • #2
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For what values of x does the series:

[tex]\sum_{n=1}^{\infty}x^n[/tex]

converge?
 
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  • #3
HallsofIvy
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Homework Statement


Series is:

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

Homework Equations




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.
[tex]\frac{(ln x)^n}{(ln x)^{n+1}}= \frac{1}{ln x}[/tex]
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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