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Harmonic series proof

  1. Oct 5, 2009 #1

    The harmonic series is given by: [tex]H_{n} = \sum_{i=1}^n \frac{1}{i}[/tex]

    I need to prove that for all positive integers:
    [tex]\sum_{j=1}^n H_{j} = (n+1)H_{n} -n[/tex]

    So i have
    [tex]H_{5} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{137}{60}[/tex]

    [tex]H_{5} \neq (5+1)*\frac{137}{60} -5[/tex]

    Have i missed something here?

    Please excuse my epic fail math skills...
    Last edited: Oct 5, 2009
  2. jcsd
  3. Oct 5, 2009 #2


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    Staff Emeritus
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    So for your H5 example what they want you to sum is

    H1 + H2 + H3 + H4 + H5

    When I did that I got what the problem tells you you will get
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