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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

I am pretty new with this serie I am supposed to find convergent or divergent.

\(\displaystyle \sum_{k=1}^\infty[\ln(1+\frac{1}{k})]\)

progress:

\(\displaystyle \sum_{k=1}^\infty[\ln(1+\frac{1}{k})]= \sum_{k=1}^\infty [\ln(\frac{k+1}{k})] = \sum_{k=1}^\infty[\ln(k+1)-\ln(k)]\) so we got that

\(\displaystyle \lim_{n->\infty}(\ln(2)-\ln(1))+\)\(\displaystyle (\ln(3)-\ln(2))+...+(\ln(n+1)-\ln(n))\)

and this is where I am stuck

Regards,

\(\displaystyle |\pi\rangle\)