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Math Help - Summation of fraction

  1. #1
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    Summation of fraction

    Hi Guys,

    I need a little help with this summation problem.

    Find in terms of n, the value of the following sum,



    I looked around and found this is called a harmonic series and is divergent to infinity. But the required answer is,



    Please Help! Thanks.
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  2. #2
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    Breaking it up into two simpler fractions is exactly what you do. Note that the harmonic series is only divergent when you have an infinite number of terms. But this is a series of a fininte number of terms... This is actually a telescopic series.

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  3. #3
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by mathguy80 View Post
    Hi Guys,

    I need a little help with this summation problem.

    Find in terms of n, the value of the following sum,



    I looked around and found this is called a harmonic series and is divergent to infinity. But the required answer is,



    Please Help! Thanks.
    Is...

    (1)

    ... so that is also [telescopic sum]...

    (2)

    Kind regards

    \chi \sigma
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  4. #4
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    This is very cool! I had studied a similar technique, when deriving,



    I did not know that it's called a Telescopic series! Thanks @Prove It and @chisigma.
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  5. #5
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    Quote Originally Posted by mathguy80 View Post
    This is very cool! I had studied a similar technique, when deriving,



    I did not know that it's called a Telescopic series! Thanks @Prove It and @chisigma.
    This is not a telescopic series. Here you would need to use induction or a proof-without-words, like this...

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