What does the alternating harmonic series converge to? Calculus Tests of Convergence / Divergence Harmonic Series 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# Answer link Related questions What is the Harmonic Series? How do you Find the sum of the harmonic series? How do you show that the harmonic series diverges? Why does the Harmonic Series diverge? How do you use the Harmonic Series to prove that an infinite series diverges? See all questions in Harmonic Series Impact of this question 12871 views around the world You can reuse this answer Creative Commons License