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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
    $$1-\frac{(k+2)+1}{(k+1)(k+2)}$$
    by multiplying the left fraction by (k+2) which got me nowhere.

    What am I doing wrong?
     
  2. jcsd
  3. Mar 5, 2014 #2
    disregard, I figured it out. I simply had to seperate 1/i(i+1) into 1/i - 1/(i+1)
     
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