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Math Help - Using PMI help!

  1. #1
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    Jan 2009
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    Using PMI help!

    Hi all,

    Well I went to my teacher to get help, but his method just did not work (no idea why). I'm trying to solve this:

    For all n in N (where N is the set of natural numbers) , 1/2(5) + 1/5(8) + ... + 1/(3n-1)(3n+2) = n/6n+4

    I understand the steps to PMI, but when I get to the Inductive Step P(k+1) and try to solve the equality I get completely stuck.

    I don't know what I am doing wrong, whether it be the PMI steps or otherwise. Thanks guys.
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  2. #2
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    Quote Originally Posted by teacast View Post
    Hi all,

    Well I went to my teacher to get help, but his method just did not work (no idea why). I'm trying to solve this:

    For all n in N (where N is the set of natural numbers) , 1/2(5) + 1/5(8) + ... + 1/(3n-1)(3n+2) = n/6n+4

    I understand the steps to PMI, but when I get to the Inductive Step P(k+1) and try to solve the equality I get completely stuck.

    I don't know what I am doing wrong, whether it be the PMI steps or otherwise. Thanks guys.
    for the P(k+1) you must have:

    1/2(5) +1/5(8)+.......................+1/(3n-1)(3n+2) + 1/(3n+2)(3n+5) =

    =(n+1)/6[(n+1)+4]= (n+1)/2(3n+5)........................................... ............................1

    IF (1) is satisfied then the P(k+1) step is satisfied.

    Since you already have : 1/2(5) +....................+1/(3n-1)(3n+2)= n/(6n+4) ,substitute that into (1) and you get:

    n/(6n+4) + 1/(3n+2)(3n+5) = (n+1)/2(3n+5) or:


    n/2(3n+2) + 1/(3n+2)(3n+5) = (n+1)/2(3n+5).

    DO THE calculations and you will see that the equation is satisfied
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