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Math Help - Need help balancing an Induction Proof

  1. #1
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    Need help balancing an Induction Proof

    (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
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    Quote Originally Posted by math61688 View Post
    (k/k+1)+ (1/(k+1)(k+2)) = (k+1)/(k+1)+1


    The right side must be \frac{k+1}{(k+1)+1}=\frac{k+1}{k+2} , but then:

    \frac{k}{k+1}+\frac{1}{(k+1)(k+2)}=\frac{1}{k+1}\l  eft(k+\frac{1}{k+2}\right)=\frac{1}{k+1}\left(\fra  c{k^2+2k+1}{k+2}\right) =\frac{1}{k+1}\cdot \frac{(k+1)^2}{k+2}=\frac{k+1}{k+2}

    Tonio


    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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  3. #3
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    thanks for the help!
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