What does the alternating harmonic series converge to?

1 Answer
Wataru
Sep 20, 2014

Alternating Harmonic Series

#sum_{n=1}^infty(-1)^{n-1}/n=ln2#

Since

#ln(1-x)=-sum_{n=1}^infty{x^n}/n#,

by setting #x=-1#,

#ln2=-sum_{n=1}^infty{(-1)^n}/n=sum_{n=1}^infty(-1)^{n-1}/n#

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