Friday, 17 May 2013

real analysis - Finding limntoinftysum2nk=nfrac1k

Let an be defined via
an=2nk=n1k. Compute, lim.



I have an handwavy argument that since \lim_{n\to\infty}\left(\sum_{k=1}^n \frac{1}{k} - \log(n) \right) = \gamma, where \gamma is the Euler-Mascheroni constant, I think that the limit above is \log(2), but I am a bit confused. Can someone help me with this? Thanks!

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