September 24th, 2008, 06:55 PM  #1 
Newbie Joined: Sep 2008 Posts: 1 Thanks: 0  Target Values & Series
Consider the series 1(1/2)+(1/3)(1/4)+...+((1)^(k1))/k+...prove that there is a target value T (whether we know what it is or not) which is the VALUE of this series. Can anyone help me out? I have a value of 2/3 and where n=10 value is within .001. But not quite sure what this question is asking me to do??? 
September 25th, 2008, 03:04 AM  #2 
Site Founder Joined: Nov 2006 From: France Posts: 824 Thanks: 7  Re: Target Values & Series
The problem asks you to show that this series is convergent. In order to do this, you can use the alternate series theorem: consider sequence (u_n) of real numbers such that (1)^(n+1)u_n >=0, limit u_n = 0 and (u_n) is decreasing. Then sum(u8n) converges.


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