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Help with induction proof

  1. Feb 27, 2012 #1
    Hello there, I'm having trouble proving this by induction

    1. The problem statement, all variables and given/known data
    [itex]\frac{1}{1(2)} + 1\frac{1}{2(3)}+...+\frac{1}{n(n+1)} = \frac{n}{n+1}[/itex]

    2. Relevant equations
    For the base case n=1

    [itex]\frac{1}{1(2)}=\frac{1}{1+1} = \frac{1}{2} = \frac{1}{2}[/itex]

    [itex]\frac{k}{k+1} + \frac{1}{(k+1)(k+2)}[/itex] <- the second term would be the next integer
    3. The attempt at a solution
    [itex]\frac{1}{1(2)}+ \frac{1}{2(3)}+\frac{1}{k(k+1)} + \frac{1}{(k+1)(k+2)} = \frac{k+1}{(k+1)+1} = \frac{k}{k+2} + \frac{1}{k+2}[/itex]

    I don't know where to go from here, any help would be appreciated
  2. jcsd
  3. Feb 27, 2012 #2


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    Science Advisor
    Homework Helper

    welcome to pf!

    hi welcome to pf! :wink:
    ok, now put the whole thing over (k+1)(k+2) …

    what do you get? :smile:
  4. Feb 27, 2012 #3
    oh, thanks very much! was pretty obvious now!
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