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Summation problem

  1. Nov 9, 2008 #1
    1. The problem statement, all variables and given/known data

    Let f(n) = 1/2 + 1/3 + .... + 1/n
    Show that f(n) is not an integer for any positive integer n


    3. The attempt at a solution

    I think that rearraning/breaking down the statement might be easier than applying a theorem since it seems like a simpler problem. Simply arranging the terms got pretty messy so I think the best method is to try to find an integer C such that C x f(n) is not a integer for any value of n. I tried different ways of computing such an integer C, such as taking C to be (n-1)! or something similar for that the summation will give a bunch of integers plus one term that is not an integer but I failed to find such a value. Hopefully someone can help me out over here. Thanks.
     
  2. jcsd
  3. Nov 9, 2008 #2
    I'm a little rusty on this stuff but couldn't we solve this using induction?
     
  4. Nov 9, 2008 #3
    The funny thing is [tex]f(1)=1/1[/tex] and [tex]1[/tex] is an integer. But, aside from that, IDK.
     
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