1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Telescoping sum issues

  1. Apr 1, 2008 #1
    1. The problem statement, all variables and given/known data

    The problem asks me to express the sum of the series as a telescoping sum, then find whether it is convergent or divergent. Ok, I get that and how it works and all, but the examples they give in the book are stupid and i on spring break this week so no office hours for professors.

    2. Relevant equations
    Here it is:

    2/(n^2 + 4n + 3)

    I know, easy, but I don't get how to do it.....the easy ones stump me.
    3. The attempt at a solution

    I rewrote it like this:
    (1/2)(2/n+3) - 2/n+1)

    But the terms do not cancel when I do this. Plus it is an even question so I do not know the solution.
  2. jcsd
  3. Apr 1, 2008 #2
    I can tell :rofl:

    You didn't do the partial fractions right; This is apparent by plugging in n=0 to the original and what you got: [tex]\frac{2}{n^2+4n+3}=\frac{1}{n+1}-\frac{1}{n+3}[/tex]. These terms WILL cancel at some point. Write out the first 5 or so terms of the series and you will see this.
  4. Apr 1, 2008 #3
    Well I did that, and they started cancelling, and I got

    (1 - 1/3) + (1/2 - 1/4) + (1/3 - 1/5) + (1/4 - 1/6) + (1/5 - 1/7)

    I cancelled the 1/3, 1/4, and the 1/5 out, but where do I go from there?

    Sorry im kind of retarted
  5. Apr 1, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    Now write a few more terms and cancel the 1/6 and 1/7. What terms don't cancel? I kind of have faith that you aren't THAT retarded.
  6. Apr 2, 2008 #5


    User Avatar
    Science Advisor

    What you want to do is make sure that, for each "-1/(n+1)", there exist an m so that its "1/(m+3)" cancels it. That is, given an integer n, what m will make 1/(m+3)= 1/(n+1)?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook