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Find all the real values of $x$ for which $\sum_1^{\infty}(x^n/n)$ converges.

I began with the ratio test to get $nx/(n+1)$ but I'm not sure where to go next. I think I'm supposed to use Leibniz's Theorem at some point?

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    Yes, sorry that was a typo, I'll correct it.2012-11-25

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$a_n:=\frac{x^n}{n}\Longrightarrow \left|\frac{a_{n+1}}{a_n}\right|=\left|\frac{x^{n+1}}{n+1}\frac{n}{x^n}\right|=|x|\frac{n}{n+1}\xrightarrow [n\to\infty]{}|x|$

Thus, the series converges for $\,-1 , and it's easy to see that it also converges for $\,x=-1\,$ (Leibnitz series)

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    OK I see what @DonAntonio meant now.2012-11-25