Results 1 to 4 of 4

Math Help - [SOLVED] Prove this with induction

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    70

    [SOLVED] Prove this with induction

    3.2^n<n! for any positive interger n greater than 4

    i did the base step

    3\times2^5<5!
    96<120

    now the n+1 step, i can do some of but get stuck

    3\times2^{n+1}<(n+1)!
    3\times2^n\times2<n!\times(n+1)

    what do i do from here? thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,793
    Thanks
    1688
    Awards
    1
    Quote Originally Posted by Rapid_W View Post
    3.2^n<n! for any positive interger n greater than 4

    i did the base step

    3\times2^5<5!
    96<120
    At this point you assume that 3\cdot 2^n <n! is a true statement.
    Next we take a look at 3\cdot 2^{n+1}

    But that is 2\cdot 3\cdot 2^n <2n! from the inductive assumption.
    How does 2 compare with n+1? Now you have one more step.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2008
    Posts
    70
    Did you get 2n! because all you have done to the LHS is essentially multiply by two?

    Also is the next step just stating that 2<n+1 when n<4?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,793
    Thanks
    1688
    Awards
    1
    Quote Originally Posted by Rapid_W View Post
    Did you get 2n! because all you have done to the LHS is essentially multiply by two?
    Also is the next step just stating that 2<n+1 when n<4?
    We know that \color{blue}3\cdot 2^n<n!
    Looking at 3\cdot 2^{n+1}=2\cdot{\color{blue}3\cdot 2^n}<2\cdot\color{blue}n!.

    Because 2 < 4 < n < n + 1 and (n+1)n!=(n+1)! you are done.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: June 29th 2010, 12:10 PM
  2. [SOLVED] Prove using mathematical induction
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: March 20th 2010, 11:41 PM
  3. Replies: 4
    Last Post: May 15th 2009, 12:16 PM
  4. prove by induction
    Posted in the Algebra Forum
    Replies: 3
    Last Post: June 19th 2008, 08:09 AM
  5. Prove by Induction
    Posted in the Algebra Forum
    Replies: 5
    Last Post: May 30th 2008, 11:16 AM

Search Tags


/mathhelpforum @mathhelpforum