
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 12th, 2017, 01:00 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 01:02 PM. 
November 12th, 2017, 02:22 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 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, 02:53 PM  #3 
Senior Member Joined: Aug 2012 Posts: 2,342 Thanks: 731 
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 03:49 PM. 

Tags 
limit, show 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
upper limit = lower limit implies convergence  zylo  Calculus  13  May 31st, 2017 12:53 PM 
Show that a continuous derivative is a uniform limit  Jeh  Real Analysis  1  August 3rd, 2012 04:27 PM 
Show set has no limit points  xsw001  Real Analysis  1  October 24th, 2010 02:18 PM 
want to show that show that two infinite summations R equal  notnaeem  Real Analysis  4  August 16th, 2010 12:32 PM 
when should we evaluate left limit and right limit?  conjecture  Calculus  1  July 24th, 2008 01:14 PM 