Test the convergence of $\displaystyle \sum_{n=0}^\infty \frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k-1}}{\ln (k)}$.

I try to use ratio test but I am stuck in summing up the numerator part.

Can anyone help me?

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- Feb 16th 2011, 12:21 AMproblemseries
Test the convergence of $\displaystyle \sum_{n=0}^\infty \frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k-1}}{\ln (k)}$.

I try to use ratio test but I am stuck in summing up the numerator part.

Can anyone help me? - Feb 16th 2011, 12:27 AMchisigma
The first step in order to extablish if a series $\displaystyle \displaystyle \sum_{n=0}^{\infty} a_{n}$ converges or not is to verify the $\displaystyle \displaystyle \lim_{n \rightarrow \infty} a_{n}$. How can we say in this case?...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Feb 16th 2011, 05:15 AMCaptainBlack