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Math Help - help with proof involving harmonic sequence

  1. #1
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    help with proof involving harmonic sequence

    Prove that:
    H1+H2+...+Hn = (n+1)Hn-n
    I'm totally lost on this problem. I know it involves using induction in some way, but I have no clue how to tackle it.
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  2. #2
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    Re: help with proof involving harmonic sequence

    Hey Otto45.

    What is the definition of H_n?
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  3. #3
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    Re: help with proof involving harmonic sequence

    Judging by the title and the question, H_n should be the n^{th} partial sum of the harmonic series.
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  4. #4
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    Re: help with proof involving harmonic sequence

    Hi Otto,

    Undoubtedly you know about integration by parts which applies to the integral of a product. The discrete analog to this is summation by parts which applies to the sum of a product. One proof of your equation uses this summation by parts. Here it is:

    help with proof involving harmonic sequence-mhfharmonic.png
    Thanks from Otto45
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