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Math Help - series convergence and sum

  1. #1
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    series convergence and sum

    I know this series converges by graphing it, but im confused on how to go about solving it and computing the sum.

    the sum from n=2 to INF of 2/((4n^2) - 1)
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  2. #2
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    2=(2n+1)-(2n-1).

    It's a telescoping series.
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  3. #3
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    Im still kind of lost, im taking this class through the mail, so i do not have a teacher to help out at all. Im trying to study for the final and i struggled through sequences and series.
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  4. #4
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    Quote Originally Posted by mikemurphy View Post
    Im still kind of lost, im taking this class through the mail, so i do not have a teacher to help out at all. Im trying to study for the final and i struggled through sequences and series.
    a telescopic series is one which has (for example) sum of two terms in n-th place, both of which cancel with one term from (n-1)th and (n+1)th each respectively. finally you can just see what is the sum ... try it ... it is straightforward.
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