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Finding a of n from Sn partial sum

  1. Sep 28, 2013 #1
    1. The problem statement, all variables and given/known data

    suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1

    2. Relevant equations

    Sn= (-2n+9)/(6n+15

    3. The attempt at a solution
    So I attempted to subtract S(n-1) from S(n) to get each term for an and got the following terms
    a2=8/9
    3=-8/3
    4=8/9
    5=8/45
    6=8/105
    7=8/189
    8=8/297
    How am I supposed to come up with a generalized expression from these terms, or am I wrong from the first step of doing S(n)-S(n-1) to get those terms for an? The only pattern I can recognize is that after a4, the difference of the denominators increase by 24 from one term to the next.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Sep 28, 2013
  2. jcsd
  3. Sep 28, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    ##S_{n}-S_{n-1}=a_n##. So take your expression for ##S_n## and subtract the same expression with n-1 substituted for n. Putting numbers in isn't the way to do it.
     
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