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Induction Hypothesis:

  1. Dec 7, 2003 #1
    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 some k > 10. 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 ……(b) because

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





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

    thanks
     
  2. jcsd
  3. Dec 7, 2003 #2
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