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Homework Help: Practice exam question on series

  1. Nov 29, 2017 #1
    1. The problem statement, all variables and given/known data
    Find the value of the sum

    (Infinity)
    Σ 2/((n+1)(n+3))
    (n=1)

    2. Relevant equations

    Integral test

    Partial Sum Formula = k/2 (a_1 + a_k)

    3. The attempt at a solution

    Admittedly I started off this problem the wrong way. I used the integral test thinking I might get an answer there, but only found that it converged, not that it was equal to what I got. A little puzzled at the usage of 'partial sum formula' but I do not recognize it. Looking through my book's index, 'partial sum' isn't even mentioned. I flipped through the relevant chapters and didn't see mention of it either.

    But, it still confuses me as to how it works. If I plug in an arbitrarily large number, like 1 billion, I get well above the correct answer, which was marked as 5/6. How do I properly apply the Partial Sum formula?
     
  2. jcsd
  3. Nov 29, 2017 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Write it as a "telescoping series".
     
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