Results 1 to 4 of 4

Math Help - Help with a proof by induction

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Ohio
    Posts
    14

    Help with a proof by induction

    Prove the following using the principle of mathematic induction.
    n! > n^2, for all integers n >= 4.

    I am especially having trouble with the inductive step. Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,570
    Thanks
    1428

    Re: Help with a proof by induction

    Quote Originally Posted by Walshy View Post
    Prove the following using the principle of mathematic induction.
    n! > n^2, for all integers n >= 4.

    I am especially having trouble with the inductive step. Thanks for your help.
    Can you please show us what you have done? Then we can set you in the right direction.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Ohio
    Posts
    14

    Re: Help with a proof by induction

    Basis Step: 4!>4^2, 24>16 - that works.
    Inductive step: Assume k! >k^2
    Goal: (k+1)! > (k+1)^2
    = k+1(k!) > k^2+2k+1
    stuck here.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,570
    Thanks
    1428

    Re: Help with a proof by induction

    Quote Originally Posted by Walshy View Post
    Basis Step: 4!>4^2, 24>16 - that works.
    Inductive step: Assume k! >k^2
    Goal: (k+1)! > (k+1)^2
    = k+1(k!) > k^2+2k+1
    stuck here.
    The way you set out these problems needs work - you need to start on one side of your statement and go through a series of arguments to get to the other side. But anyway, your logic is right at least...

    \displaystyle \begin{align*} ( k + 1 ) ! &= (k + 1)k! \\ &> (k + 1)k^2 \\ &> (k + 1)^2 \textrm{ since } k^2 > k + 1 \end{align*}

    It's up to you to prove \displaystyle \begin{align*} k^2 > k + 1 \end{align*} in our region
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof by Induction
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 26th 2011, 06:48 AM
  2. proof by induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 17th 2010, 07:11 AM
  3. Proof by induction
    Posted in the Algebra Forum
    Replies: 8
    Last Post: July 7th 2009, 01:42 AM
  4. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  5. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM

Search Tags


/mathhelpforum @mathhelpforum