(2n)?$

Asked Nov 10 '20 at 23:26

Active Nov 10 '20 at 23:38

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I feel like $\lim_{n \to \infty} 1+ 1/2 + 1/3 +\dots +1/n$ should be equal with 2, but I'm not sure. Any help is hugely appreciated, because I've never done such exercises before and I couldn't find how to approach them.

asked Nov 10 '20 at 23:26

aneys

Harmonic series diverges – J. W. Tanner Nov 10 '20 at 23:28
1

The first is $\infty$, and the second is $\ln 2$. – uniquesolution Nov 10 '20 at 23:29
And the second is the Newton-Mercator expansion of $\ln 2$. – anon Nov 10 '20 at 23:29
Thank you. How can I prove the limit of the second one is ln 2? – aneys Nov 10 '20 at 23:32

What is $\lim_{n \to \infty} 1+ 1/2 + 1/3 +\dots +1/n$. What is $\lim_{n \to \infty} 1- 1/2 + 1/3 +\dots +1/(2n-1)-1/(2n)?$

0 Answers0