Results 1 to 3 of 3

Math Help - stuck on two mathematical induction problems

  1. #1
    Newbie
    Joined
    Mar 2012
    From
    San diego
    Posts
    1

    stuck on two mathematical induction problems

    Hello,

    I have been trying to solve this problem for the last hour and haven't gotten anywhere. Got any ideas?

    #1
    (1 - 1/2)(1 - 1/2^2)...(1-1/n^2)=n+1/2n


    Prove: (1-(1/(n+1)^2) + (n+1)/2n = (n+2)/(2n+2) for all integers >=2 (greater/equal)

    #2
    2^n < (n+2)!, for all integers n >= 0
    Last edited by dotman1989; March 12th 2012 at 09:44 PM. Reason: misformat
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2011
    From
    Crna Gora
    Posts
    420
    Thanks
    64

    Re: stuck on two mathematical induction problems

    Quote Originally Posted by dotman1989 View Post
    Hello,

    I have been trying to solve this problem for the last hour and haven't gotten anywhere. Got any ideas?

    #1
    (1 - 1/2)(1 - 1/2^2)...(1-1/n^2)=n+1/2n


    Prove: (1-(1/(n+1)^2) + (n+1)/2n = (n+2)/(2n+2) for all integers >=2 (greater/equal)

    #2
    2^n < (n+2)!, for all integers n >= 0
    #2

    1) n=0 ; 2^0 < 2!

    2) \text{suppose that :} 2^n < (n+2)!

    3) \text{we have to prove :} 2^{n+1} < (n+3)!

    2 \cdot 2^n < 2 \cdot (n+2)! <  (n+3)\cdot (n+2)!=(n+3)!

    \text{hence:}

     2^{n+1} < (n+3)!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,569
    Thanks
    1410

    Re: stuck on two mathematical induction problems

    Quote Originally Posted by dotman1989 View Post
    Hello,

    I have been trying to solve this problem for the last hour and haven't gotten anywhere. Got any ideas?

    #1
    (1 - 1/2)(1 - 1/2^2)...(1-1/n^2)=n+1/2n
    Your real problem here, is that the "theorem", as stated, is not true. Specifically, if n= 2, the left side is (1- 1/2)(1- 1/4)= 1- 1/2- 1/4+ 1/8= 8/8- 4/8- 2/8+ 1/8= 9/8- 6/8= 3/8 while the right side is 2+ 1/4= 9/4, not 3/8.

    Prove: (1-(1/(n+1)^2) + (n+1)/2n = (n+2)/(2n+2) for all integers >=2 (greater/equal)

    #2
    2^n < (n+2)!, for all integers n >= 0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Four mathematical induction problems
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 3rd 2010, 03:17 PM
  2. Replies: 10
    Last Post: June 29th 2010, 12:10 PM
  3. Replies: 1
    Last Post: April 19th 2010, 12:53 PM
  4. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 09:33 PM
  5. Mathematical induction problems
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 8th 2007, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum