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Series Convergence and Divergence

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data
    Determine if the following series converges or diverges. If it converges determine its sum.
    Ʃ1/(i2-1) where the upper limit is n and the index i=2


    2. Relevant equations

    The General Formula for the partial sum was given:
    Sn=Ʃ1/(i2-1)=3/4-1/(2n)-1/(2(n+1)

    3. The attempt at a solution
    I have no idea where to start. I tried to get the General Formula, but I am really confused as to how to even start. I tried to split the function with partial fractions and somehow got 1/(2(i+1))-1/(2(i-1))
     
  2. jcsd
  3. Nov 27, 2011 #2
    oops! I got it. It's a telescopic sum. I need to open my eyes a little more.
     
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