Results 1 to 4 of 4

Math Help - Induction proof

  1. #1
    Newbie
    Joined
    Mar 2007
    Posts
    21

    Induction proof

    1)
    A) Find k>0 and m element of N so that 7n^3 + 13n <= kn^3 for all integers n >= m.... take k = 7.0052 and find the corresponding value of m

    B) find k > 0 and m element of N so that n^3 - 3n >= kn^3 for all integers
    n >= m

    2) Find an example of each of the following
    A) A convergent sequence of rational numbers having an irrational limit
    B) A convergent sequence of irrational numberse having a rational limit.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    For #2
    A) Let [x_1]=1. Then if n>1, let [x_n]={1+(2/[x_(n-1])}/2.


    B) Let [y_n]=sqrt(2)/n
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2007
    Posts
    21
    Do you have any ideas on #1?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by learn18 View Post
    1)
    A) Find k>0 and m element of N so that 7n^3 + 13n <= kn^3 for all integers n >= m.... take k = 7.0052 and find the corresponding value of m
    .
    You can take k=8.

    7n^3+13n<=8n^3 for sufficiently large n.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof by Induction
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 11th 2011, 07:22 AM
  2. Proof by Induction
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 16th 2010, 12:09 PM
  3. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  4. Proof by Induction??
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 6th 2008, 03:55 PM
  5. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM

Search Tags


/mathhelpforum @mathhelpforum