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Proof by induction - fractions

  1. Mar 5, 2014 #1
    1. The problem statement, all variables and given/known data
    I have been working on this proof for a few hours and I can not make it work out.

    $$\sum_{i=1}^{n}\frac{1}{i(i+1)}=1-\frac{1}{(n+1)}$$

    i need to get to $$1-\frac{1}{k+2}$$

    I get as far as $$1-\frac{1}{k+1}+\frac{1}{(k+1)(k+2)}$$
    then I have tried $$1-\frac{(k+2)+1}{(k+1)(k+2)}$$ bu multiplying the left fraction by (k+2) which got me nowhere.

    What am I doing wrong?
     
  2. jcsd
  3. Mar 5, 2014 #2

    vela

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    You have a sign error. If you can't find it, try expanding
    $$1-\frac{(k+2)+1}{(k+1)(k+2)}$$ and compare it to what you started with.
     
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