Results 1 to 2 of 2

Thread: mathematical induction

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    166

    mathematical induction

    Prove that $\displaystyle 3^n \geq 3n$.
    If $\displaystyle n=1$, then $\displaystyle 3^1=3(1)$. Clearly, this is true.
    Assume $\displaystyle n=k$ and $\displaystyle 3^k \geq 3k$.
    If $\displaystyle n=k+1$, then $\displaystyle 3^{k+1}=3^k 3$
    I am stuck here. Can someone explain how to show $\displaystyle 3^{k+1} \geq 3(k+1)$? Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by dori1123 View Post
    Prove that $\displaystyle 3^n \geq 3n$.
    If $\displaystyle n=1$, then $\displaystyle 3^1=3(1)$. Clearly, this is true.
    Assume $\displaystyle n=k$ and $\displaystyle 3^k \geq 3k$.
    If $\displaystyle n=k+1$, then $\displaystyle 3^{k+1}=3^k 3$
    I am stuck here. Can someone explain how to show $\displaystyle 3^{k+1} \geq 3(k+1)$? Thank you.
    note that $\displaystyle k \ge 1$, so that

    $\displaystyle 3^{k + 1} = 3 \cdot 3^k \ge 3 \cdot 3k > 3k + 3k \ge 3k + 3 = 3(k + 1)$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mathematical Induction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Aug 31st 2010, 03:31 PM
  2. Mathematical induction
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Aug 30th 2010, 05:54 AM
  3. Replies: 10
    Last Post: Jun 29th 2010, 12:10 PM
  4. mathematical induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Apr 13th 2009, 05:29 PM
  5. Mathematical Induction
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Mar 18th 2009, 08:35 AM

Search Tags


/mathhelpforum @mathhelpforum