Results 1 to 3 of 3

Math Help - Stuck on proof by induction

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    17

    Stuck on proof by induction

    Hey, Stuck on this proof by induction question. I can get so far but not sure where to go after.

    3*2^n < n! when n>4

    Basis for Induction

    3*2^5 < 5!

    96 < 120

    Induction Step

    We assume 3*2^n <n! when n>4

    We need to prove that 3*2^n^+^1 < (n+1)!

    (n+1)! = (n+1)n!

    (3*2^n)(n+1)<(n+1)n!

    (3*2^n)(n+1)<(n+1)!

    This is as far as I can get Any help would be appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by dtwazere View Post
    Hey, Stuck on this proof by induction question. I can get so far but not sure where to go after.

    3*2^n < n! when n>4

    Basis for Induction

    3*2^5 < 5!

    96 < 120

    Induction Step

    We assume 3*2^n <n! when n>4

    We need to prove that 3*2^n^+^1 < (n+1)!

    (n+1)! = (n+1)n!

    (3*2^n)(n+1)<(n+1)n!

    (3*2^n)(n+1)<(n+1)!

    This is as far as I can get Any help would be appreciated!

    3\cdot 2^{n+1}=2(3\cdot 2^n)<2\cdot n! < (n+1)n!=(n+1)! , the last inequality being true since n+1>2 ...

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,390
    Thanks
    1476
    Awards
    1
    Recall that n>1 then n+1>2.

    Start with 3\cdot 2^{n+1}=[3\cdot 2^{n}](2)<[n!](?)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stuck on proof by induction
    Posted in the Discrete Math Forum
    Replies: 12
    Last Post: October 19th 2011, 07:16 AM
  2. Proof by induction stuck at very end!!
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 25th 2009, 03:38 AM
  3. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  4. Proof by induction stuck on a sum:help:
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 15th 2008, 10:27 AM
  5. Induction proof...I'm stuck!
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 18th 2008, 10:24 AM

Search Tags


/mathhelpforum @mathhelpforum