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Recursive sequence terms don't cancel

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data

    The following series is a telescopic series. Find the exact sum of the series by performing a partial fraction decomposition and generalizing the formula for the nth partial sum Sn.

    problem.png

    2. Relevant equations



    3. The attempt at a solution

    3n + 2 = A(n+1)(n+2) + B(n)(n+2) + C(n)(n+1)
    n = 0 → 2 = 2A → A = 1
    n = -1 → -1 = -B → B = 1
    n = -2 → -4 = 2C → C = -2

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

    => Sn = ... = 1 + 1/2 + 1/3 + ... + 1/n + 2/3 + 2/5 + 2/7 + ... + 1/(2n + 1)

    I don't see the terms cancel. Did i do something wrong?

    Thanks
     
    Last edited: Oct 17, 2011
  2. jcsd
  3. Oct 17, 2011 #2
    You forgot about the minus, dude! C=-2 :D
     
  4. Oct 17, 2011 #3
    Ah, sorry about that, i did have a minus in my original work, typo o_o
     
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