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 November 12th, 2017, 02:00 PM #1 Newbie   Joined: Oct 2017 From: Here Posts: 13 Thanks: 0 How to show the following limit is 0? I have the series 1/(n*(-1)^n). I believe the limit is 0, but I'm not sure how to show that. Thanks! Last edited by Mathmatizer; November 12th, 2017 at 02:02 PM.
 November 12th, 2017, 03:22 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,031 Thanks: 2342 Math Focus: Mainly analysis and algebra It's the alternating harmonic series isn't it? Convergence guaranteed because the sequence $|a_n|$ is decreasing and $a_n$ is alternating. Thanks from topsquark and SenatorArmstrong
 November 12th, 2017, 03:53 PM #3 Senior Member   Joined: Aug 2012 Posts: 1,628 Thanks: 413 The sum is ln 2. https://en.wikipedia.org/wiki/Harmon...armonic_series ps -- OP said series. The limit of the sequence is of course 0. Thanks from topsquark Last edited by Maschke; November 12th, 2017 at 04:49 PM.

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