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Harmonic Sum

  1. Jun 15, 2006 #1
    How do I show that [tex]\sum_1^n\frac{1}{k}[/tex] is not an integer for n>1? I tried bounding them between two integrals but that doesn't cut it. I know that [tex]\sum_1^n\frac{1}{k}=\frac{(n-1)!+n(n-2)!+n(n-1)(n-3)!+...+n!}{n!}[/tex] but I can't get a contradiction.
  2. jcsd
  3. Jun 15, 2006 #2


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    Last edited by a moderator: Apr 22, 2017
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