Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Plato

Math Help - Use induction to verify the inequality

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    NY
    Posts
    4

    Use induction to verify the inequality

    The problem:
    Use induction to verify the inequality
    2n+1 <= 2n | n >= 3

    My work thus far:
    Base case n = 3:
    2(3) + 1 <= 23
    7 <= 8

    Inductive step:
    Assume 2n+1 <= 2n is true for some n >= 3.
    Prove 2(n+1) + 1 <= 2(n+1)(2n+1)+2 <= 2*2n
    ...

    I am not sure what to do from here. Replacing the 2n leaves me with 4n+2 and replacing the 2n+1 leaves me with 2n+2. I thought that with inequalities I am suppose to replace terms in the greater expression with terms from the lesser expressions so that the resulting expression equals the lesser expression or vice versa. However, with this neither replacement results in an equivalent expressions.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,639
    Thanks
    1592
    Awards
    1

    Re: Use induction to verify the inequality

    Quote Originally Posted by AltF4 View Post
    The problem:
    Use induction to verify the inequality
    2n+1 <= 2n | n >= 3

    My work thus far:
    Inductive step:
    Assume 2n+1 <= 2n is true for some n >= 3.
    Prove 2(n+1) + 1 <= 2(n+1)(2n+1)+2 <= 2*2n...
     \begin{align*}2^{N+1}&=2\cdot 2^N \\&\ge 2(2N+1)\\&=4N+2\\&>2(N+1)+1\end{align*}
    Thanks from AltF4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Induction: an inequality
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: June 16th 2011, 06:42 PM
  2. Induction Inequality
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 17th 2011, 01:47 PM
  3. induction inequality
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: February 3rd 2010, 04:09 AM
  4. induction inequality
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 26th 2008, 08:46 AM
  5. [SOLVED] Verify an inequality/integral value
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 27th 2008, 11:41 AM

Search Tags


/mathhelpforum @mathhelpforum