Results 1 to 4 of 4

Math Help - Induction problem

  1. #1
    Newbie
    Joined
    Jun 2008
    Posts
    10

    Induction problem

    Hey,

    I need to proove by Induction that k^3+3k^2+2k devided by 6 without residue.

    thanks
    omri
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by omrimalek View Post
    Hey,

    I need to proove by Induction that k^3+3k^2+2k devided by 6 without residue.

    thanks
    omri
    Have you done everything up to the induction step?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
    From
    Taguig City, Philippines
    Posts
    1,026
    Quote Originally Posted by omrimalek View Post
    Hey,

    I need to proove by Induction that k^3+3k^2+2k devided by 6 without residue.

    thanks
    omri
    you can actually check that k^3+3k^2+2k = k(k+1)(k+2) and for any natural number k, one of them is even, and one is divisible by 3. thus, it must be divisible by 6.

    by induction:
    for k=1: 1 + 3 + 2 = 6

    suppose true for n < k+1

    for n=k+1: (k+1)^3 + 3(k+1)^2 + 2(k+1) =k^3+3k^2+3k+1+3k^2+6k+3+2k+2

    =k^3+6k^2+11k+6 = k^3 + 3k^2 + 2k  + 3k^2 + 9k + 6

    =k(k^2+3k+2) + 3(k^2+3k+2) = (k+3)(k^2+3k+2)=(k+3)(k+2)(k+1)
    which is similar to the equation above..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jun 2008
    Posts
    10

    i did "n+1" step

    and got 3k^2+9kand i dont know how to proove that it divided by 6
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Another induction problem help
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 12th 2012, 05:57 PM
  2. Induction Problem
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: August 26th 2010, 06:00 AM
  3. induction problem
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: May 17th 2010, 01:02 AM
  4. induction problem,
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 7th 2009, 06:57 AM
  5. induction problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 26th 2008, 01:04 PM

Search Tags


/mathhelpforum @mathhelpforum