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Mathematical induction

  1. Dec 5, 2003 #1
    Induction Hypothesis:

    In fact pa is true for all integers n greater than a particular base value and you should complete the proof given below to use the principle of mathematical induction to prove this.

    pa : n-2 < (n^2 – 3n)/12

    Base case is n = 14
    Because: n-2 < (n^2 – 3n)/12
    14-2 < (196-42)/12
    12 < 154/12
    12 < 12.83

    Inductive step
    Inductive Hypothesis : Assume pa(k) is true for k > 14. Thus k-2 <(k^2 – 3k)/12.

    We must prove that pa(k+1) is true i.e. that (k+1)-2 < ((k+1)^2 – 3(k+1))/12

    Now to prove such an inequality we always start with the more complicated side:
    ((k+1)^2 – 3(k+1))/12 = (k^2 + 2k +1 – 3k – 3)/12

    = (k^2 – 3k)/12 + (2k-2)/12

    > ....?... + (2k-2)/12 ____because

    > ......??......... because

    the dotted white line need to be filled in and the because u have to give reasons....

    This is the question i have been given to do although no idea on how to finish it any ideas anyone ?


    ok i changed it to 14 although not sure yet on how to finish it, this for me is just baffling
    Last edited: Dec 7, 2003
  2. jcsd
  3. Dec 7, 2003 #2
    It should be "Assume pa(k) is true for some k >= 14 "

    What does the induction hypothesis tell you ?
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