Results 1 to 4 of 4

Math Help - mathematical induction

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    17

    mathematical induction

    1. Use math induction to show that (n2 - n + 2) is divisible by 2 for all natural numbers n.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
    Posts
    290

    Lightbulb

    the equation is n^2-n+2
    let n=1 then
    1^2-1+2=2 which is divisible by 2 hence its true for n=1.
    now let it be true for n=k therfor
    k^2-k+2=2r
    now let us consider n=k+1
    (k+1)^2-(k+1)+2
    =k^2+1+2k-k-1+2
    =[k^2-k+2]+2k
    =2r+2k
    =2(r+k) which is divisible by 2
    hence whenever it is true for k it is also true for k+1
    hence by PMI n^2-n+2 is divisible by 2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Pim
    Pim is offline
    Member
    Joined
    Dec 2008
    From
    The Netherlands
    Posts
    91
    1. Case for 1: (1^2 - 1 + 2) = 2 is divisible by 2
    2. Case for n + 1
    ((n+1)^2 - (n+1) + 2) =
    (n^2+2n+1 - n - 1 +2) =
    (n^2+n+2) =
    (n^2-n+2)+2n
    Assume (n^2-n+2) is divisible by two, which gives 2*(term + n), which evidently is divisible by 2.

    I'm not used to proving these things, so don't use this as your proof, however, this is the general idea.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    769

    Simpler answer

    n2 - n = n(n - 1)

    The product of an even number with an odd number is always even as the above equation is and dividing 2 by 2 is self evident. This completes the proof.
    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