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November 12th, 2017, 02:00 PM  #1 
Newbie Joined: Oct 2017 From: Here Posts: 19 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: 7,509 Thanks: 2514 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.

November 12th, 2017, 03:53 PM  #3 
Senior Member Joined: Aug 2012 Posts: 2,098 Thanks: 602 
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. Last edited by Maschke; November 12th, 2017 at 04:49 PM. 

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