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Math Help - Need Help Balancing Induction Problem

  1. #1
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    Need Help Balancing Induction Problem

    (k/k+1)+ (1/(k+1)(k+2)) = (k+1)/(k+1)+1

    I just need to make the left side equal to the right side. This is what I have:

    k(k+2)/(k+1)(k+2) + 1/(k+1))k+2) =(k+1)/(k+1)+1

    k(k+2)+1/(k+1)(k+2) = (k+1)/(k+1)+1
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
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    Quote Originally Posted by math61688 View Post
    (k/k+1)+ (1/(k+1)(k+2)) = (k+1)/(k+1)+1

    I just need to make the left side equal to the right side. This is what I have:

    k(k+2)/(k+1)(k+2) + 1/(k+1))k+2) =(k+1)/(k+1)+1

    k(k+2)+1/(k+1)(k+2) = (k+1)/(k+1)+1
    Well the top line in the left hand side of your last equation is...

    k(k+2) + 1 = k^2 + 2k + 1 = (k+1)^2

    So you get


    \frac{(k(k+2)+1)}{(k+1)(k+2)}  = \frac{(k+1)^2}{(k+1)(k+2)} = \frac{k+1}{k+2}.

    Which if you want to write it the way you've been doing is...

    \frac{k+1}{(k+1) + 1}
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