Results 1 to 2 of 2

Math Help - Short prove by induction

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    5

    Smile Short prove by induction

    I need to prove the following for one of my solutions in order to solve a problem:

    For n \in\mathbb{N} if n>=3^3 then 3^n > 79n^2

    Thank you in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    Have you checked that 3^{3^{3}}>79.(3^{3})^{2}?

    Then, let n \geq 3^{3} be an integer, and assume that 3^{n}>79n^{2} (induction hypothesis)

    79(n+1)^{2}=79n^{2}+79(2n)+79

    Is it true that, if n\geq 3^{3}\ , then \ 2n\leq n^{2} and 1\leq n^{2} ?

    If it's the case, 79n^{2}+79(2n)+79 \leq 79n^{2}+79n^{2}+79n^{2}=3(79n^{2})

    What can we conclude using the induction hypothesis?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove using induction (2)
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: August 13th 2011, 05:12 PM
  2. Replies: 10
    Last Post: June 29th 2010, 12:10 PM
  3. Induction to prove
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 25th 2008, 07:24 AM
  4. Prove by induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: June 18th 2008, 09:26 AM
  5. prove by induction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 12th 2007, 10:32 PM

Search Tags


/mathhelpforum @mathhelpforum