Results 1 to 2 of 2

Math Help - induction problem

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    6

    induction problem

    i think this one is pretty easy but i'm not that great with induction. any help?

    Show that 2^n > n for any integer n that is an element of Z^+.

    my attempt:

    base case - let n=1
    2^1=2 > 1 -> base case is true

    2^(n+1) > n+1
    2^n + 2 > n+1
    2^n > n-1

    statement holds true by the base case 2^1 > 1-1
    Last edited by geoffl; June 8th 2009 at 09:11 PM. Reason: added my attempt
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
    For n=1,  2^{1} = 2 > 1 .

    Now Assume  2^{k} > k for some k>1

    then  2^{k+1} = 2*2^{k} > 2k by the induction step

    and  2k = k+k > k+1 which is what we wanted to show
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another induction problem help
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 12th 2012, 04:57 PM
  2. Induction Problem
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: August 26th 2010, 05:00 AM
  3. induction problem,
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 7th 2009, 05:57 AM
  4. induction problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 26th 2008, 12:04 PM
  5. Induction problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 16th 2008, 04:41 AM

Search Tags


/mathhelpforum @mathhelpforum