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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

    Dick

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    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

    HallsofIvy

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    Staff Emeritus
    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)?
     
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