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Homework Help: Induction inequality

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    5^n + 9 < 6^n for all integers n>=2.

    2. Relevant equations


    3. The attempt at a solution
    Induction proof.

    Base Case: 5^(2) + 9 < 6^(2)
    34<36
    P(k): 5^k + 9 < 6^k
    P(k+1): 5^(k+1) + 9 < 6^(k+1)

    how do i prove p(k) can equal p(k+1)?
     
  2. jcsd
  3. Apr 16, 2010 #2

    Mark44

    Staff: Mentor

    You don't prove that P(k) = P(k+1). You assume that statement P(k) is true and use this fact to prove that statement P(k + 1) is also true.

    From your induction hypothesis (statement P(k)) you are assuming that
    5^k + 9 < 6^k

    Work with 5^(k + 1) + 9 and see what you get.
     
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