Results 1 to 2 of 2

Math Help - Induction Proof Help

  1. #1
    Newbie
    Joined
    Apr 2010
    Posts
    1

    Induction Proof Help

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

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

    P(k+1): 5^(k+1) + 9 < 6^(k+1)

    How do I complete the proof? If 5 and 6 were the same base I could understand multiplying to the common base to achieve the ^k+1, but the different bases really have thrown me off!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Mar 2010
    Posts
    36
    6^{k+1} = 6 \cdot 6^k > 6 \cdot (5^k + 9) \dots
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof using induction
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 5th 2009, 09:46 PM
  2. Induction Proof
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 5th 2009, 03:35 PM
  3. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 10:33 PM
  4. Proof by induction
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 30th 2008, 07:25 AM
  5. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 02:20 PM

Search Tags


/mathhelpforum @mathhelpforum