Results 1 to 2 of 2

Math Help - Mathematical Induction

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    124

    Mathematical Induction

    Prove that 1 + 3n ≤ 4n , for every integer n ≥ 0.


    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 bearej50 View Post
    Prove that 1 + 3n ≤ 4n , for every integer n ≥ 0.


    Where did you get stuck? This one was not that difficult. I'll just give the solution. It doesn't work for zero, you can check this.


    Define a statement P(n) by P(n):~~1 + 3n \le 4n for all integers n \ge 1

    We show that P(n) is true using mathematical induction.

    Since 1 + 3(1) = 4 \le 4(1), we have that P(1) is true.

    Assume that P(n) is true, we show that P(n + 1) holds also.

    Note that,

    \begin{array}{rcl} 1 + 3(n + 1) & = & 1 + 3n + 3 \\ & \le & 4n + 3 \\ & \le & 4n + 4 \\ & = & 4(n + 1) \end{array}

    So that 1 + 3(n + 1) \le 4(n + 1), which is P(n + 1). Thus, P(n) holds by induction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: June 29th 2010, 12:10 PM
  2. Mathematical Induction
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 7th 2010, 12:22 PM
  3. Mathematical Induction
    Posted in the Algebra Forum
    Replies: 9
    Last Post: July 8th 2009, 12:27 AM
  4. Mathematical Induction
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: February 17th 2009, 11:30 AM
  5. Mathematical Induction
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 30th 2007, 03:21 PM

Search Tags


/mathhelpforum @mathhelpforum