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Math Help - Limit of series

  1. #1
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    Limit of series

    Given Ur = 3/ (r2+3r)
    I have simplified nr=1 Ur in terms of n by expressing in partial fraction.
    Determine the value of r=1 Ur , deduce the value of r=2 U​r+1
    I just donít know how to deduce . Can anyone explain to me ?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Limit of series

    Quote Originally Posted by Ahjiao View Post
    Determine the value of r=1 Ur , deduce the value of r=2 U​r+1
    Decompose into partial fractions \dfrac{3}{r^2+3r}=\dfrac{1}{r}-\dfrac{1}{r+3} and look here:

    Convergence of the series 1 / n(n+2)
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  3. #3
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    Re: Limit of series

    If you know the value of \sum_{r=1}^{\infty}U_r, you should be able to find the value of \sum_{r=3}^{\infty}U_r. You just subtract the first two terms.

    And this new sum is the same as \sum_{r=2}^{\infty}U_{r+1}. If you're having trouble seeing it, write the first few terms of each.

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