Rate of growth of modified alternating harmonic series

Asked Jun 27 '19 at 15:56

Active Jun 27 '19 at 16:03

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I have the following series $$ \sum_{k=1}^{n} \dfrac{(-1)^{k+1}}{k} {n \choose k} $$

and wanted to find some function $f(n)$ that grew at the same rate approximately as thw sum. From looking at it graphically, it appears to be $n^{1/p}$ but I am stuck on trying to find $p$ and proving the limit

edited Jun 27 '19 at 16:03

callculus42

31,012

asked Jun 27 '19 at 15:56

wjmccann

3,383

What do you mean by $nCr(n,k)$? – callculus42 Jun 27 '19 at 16:00
That means $n$ choose $k$. I wasn't sure how to do the parenthesis notation in latex on my phone haha – wjmccann Jun 27 '19 at 16:02
I´ve made an edit. Please check if the edit is right. – callculus42 Jun 27 '19 at 16:04
Compute the first terms. This should look like the harmonic number $H_n$ (if I am not mistaken). – Claude Leibovici Jun 27 '19 at 16:08
@wjmccann There are many answers at this forum, e.g. here Also see the result of wolfram alpha. – callculus42 Jun 27 '19 at 16:12
Look up binomial inversion – Sandeep Silwal Jun 27 '19 at 17:50

Rate of growth of modified alternating harmonic series

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