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Math Help - [SOLVED] How do I find this value?

  1. #1
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    [SOLVED] How do I find this value?

    Find the value of \frac{1}{2.3} + \frac{1}{3.4} + \frac {1}{4.5} + ... + \frac{1}{50.51}

    THis is my take on the question:
    n = 49

    Using method of difference,

    f(r) = -\frac{1}{r + 2}
    f(r - 1) = -\frac{1}{r+1}
    Hence,
    f(n) - f(1 - 1) =  1 - \frac{1}{n + 2}

    When I sub n = 49 into this equation, I found \frac{50}{51} which is not the same as the answer of \frac{49}{102}

    Where have I gone wrong?
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  2. #2
    MHF Contributor
    Joined
    Sep 2008
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    West Malaysia
    Posts
    1,261
    Quote Originally Posted by mark1950 View Post
    Find the value of \frac{1}{2.3} + \frac{1}{3.4} + \frac {1}{4.5} + ... + \frac{1}{50.51}

    THis is my take on the question:
    n = 49

    Using method of difference,

    f(r) = -\frac{1}{r + 2}
    f(r - 1) = -\frac{1}{r+1}
    Hence,
    f(n) - f(1 - 1) =  1 - \frac{1}{n + 2}

    When I sub n = 49 into this equation, I found \frac{50}{51} which is not the same as the answer of \frac{49}{102}

    Where have I gone wrong?
    Hi

    Firstly , we know the general term is \frac{1}{(r+1)(r+2)}

    Then do partial fraction here , we get

    \sum^{49}_{r=1}[\frac{1}{r+1}-\frac{1}{r+2}]

    Here let f(r)=\frac{1}{r+1} , then  f(r+1)=\frac{1}{r+2}

    so

    \sum^{49}_{r=1}[f(r)-f(r+1)]

    = f(1)-f(50)

    =\frac{1}{1+1}-\frac{1}{50+1}

    Continue from here , you should get the answer .
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