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Math Help - [SOLVED] telescoping sum with a partial fraction

  1. #1
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    [SOLVED] telescoping sum with a partial fraction

    the sum from 2 to infinity of 2/(n^2 - 1)

    so first i factor the denominator

    2/((n + 1)(n - 1))

    this can expressed with partial fractions

    2/((n + 1)(n - 1)) = A/(n + 1) + B/(n - 1)

    which can be rearanged to

    2 = A(n + 1)(n - 1) + B(n + 1)(n - 1)

    now I'm stuck. I have one equation and 2 variables. I know there is something I'm forgetting how to do this.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by atompunk View Post
    the sum from 2 to infinity of 2/(n^2 - 1)

    so first i factor the denominator

    2/((n + 1)(n - 1))

    this can expressed with partial fractions

    2/((n + 1)(n - 1)) = A/(n + 1) + B/(n - 1)

    which can be rearanged to

    2 = A(n + 1)(n - 1) + B(n + 1)(n - 1)

    now I'm stuck. I have one equation and 2 variables. I know there is something I'm forgetting how to do this.
    It should rearrange to 2=A(n-1)+B(n+1)\implies 2=(A+B)n+B-A.

    Comparing coefficients, we get A+B=0 and B-A=2.

    Can you take it from here and find A and B?
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  3. #3
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    Krizalid's Avatar
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    2=(n+1)-(n-1).
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  4. #4
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    thanks
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