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Math Help - find its sum of this series

  1. #1
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    find its sum of this series

    SUM n=2_infinity (2)/(n^2 - 1)

    does this series converge or diverge?

    also, find its sum.

    Please help me with this problem. Also can u identify what type of series it is.

    thankyou.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    SUM n=2_infinity (2)/(n^2 - 1)

    does this series converge or diverge?

    also, find its sum.

    Please help me with this problem. Also can u identify what type of series it is.

    thankyou.
    2/(n+1)(n-1) = 1/(n-1) - 1/(n+1)

    This is a "Telescoping Series" write out the partial sums.

    S_2=1/1 - 1/3

    S_3=1/1-1/3+1/2-1/4 = 1+1/2-1/3-1/4

    S_4=1/1-1/3+1/2-1/4+1/3-1/5 = 1+1/2 - 1/4-1/5

    ...

    It seems the general pattern is,

    S_n= 1+1/2 - 1/n - 1/(n+1) for n>=2

    Take n--> +oo
    To find its sum.
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