Results 1 to 3 of 3

Thread: induction inequalities P1

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    45

    induction inequalities P1

    Prove using the principle of mathematical induction that

    3^n > 4n^2 +5n for n=4,5...

    thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,656
    Thanks
    14
    show your progress.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    4
    Quote Originally Posted by christina View Post
    Prove using the principle of mathematical induction that

    3^n > 4n^2 +5n for n=4,5...

    thank you!
    This is very straightforward.

    $\displaystyle 3^n>4n^2+5n$ ?

    If this is true, we try to use it to prove if

    $\displaystyle 3^{n+1}>4(n+1)^2+5(n+1)$

    $\displaystyle (3)3^n>4(n^2+2n+1)+5(n+1)$ ?

    $\displaystyle 3^n+(2)3^n>4n^2+4(2n)+4+5n+5$ ?

    $\displaystyle 3^n+[(2)3^n]>4n^2+5n+[4(2n)+9]$

    Therefore, we only need ask if

    $\displaystyle 2(3^n)>4(2n)+9,\ n\ \ge\ 4$

    $\displaystyle 3^n+3^n>4n+4.5+4n+4.5$

    As $\displaystyle n^2>n$ and $\displaystyle 5n>4.5$, for n=4 and above,

    only the first term needs to be tested.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Induction with Inequalities help
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Jul 17th 2010, 11:32 AM
  2. induction inequalities P3
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Feb 13th 2010, 05:37 PM
  3. induction inequalities P2
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Feb 13th 2010, 05:14 PM
  4. Induction and Inequalities
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Oct 1st 2009, 05:37 PM
  5. Verifying inequalities with induction
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Sep 28th 2009, 03:58 PM

Search Tags


/mathhelpforum @mathhelpforum