My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum

LinkBack Thread Tools Display Modes
September 24th, 2008, 06:55 PM   #1
Joined: Sep 2008

Posts: 1
Thanks: 0

Target Values & Series

Consider the series 1-(1/2)+(1/3)-(1/4)+...+((-1)^(k-1))/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???
mathjunkie is offline  
September 25th, 2008, 03:04 AM   #2
Site Founder
julien's Avatar
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.
julien is offline  

  My Math Forum > College Math Forum > Real Analysis

series, target, values

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
is this series valid for all real values xamdarb Calculus 2 March 14th, 2014 06:34 PM
Compound Interest and Target projections in Excel redliner74 Economics 3 July 17th, 2013 11:04 PM
Probability with dice and target numbers Bringer23 Advanced Statistics 1 June 13th, 2012 11:24 PM
Not sure about the increased sales target tomb Economics 5 November 16th, 2011 10:06 AM
Geometric series/target of series/etc... clooneyisagenius Real Analysis 1 January 30th, 2008 12:50 AM

Copyright © 2019 My Math Forum. All rights reserved.