Results 1 to 2 of 2

Math Help - Question on the principle of induction. Proof of divisibility

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    26

    Question on the principle of induction. Proof of divisibility

    Use the principle of mathematical induction to prove that n(n^2 +5) is divisible by 6 for all n= Z^+...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by karldiesen View Post
    Use the principle of mathematical induction to prove that n(n^2 +5) is divisible by 6 for all n= Z^+...

    Lets start at the point assume n and show that n \implies n+1

    assume that 6 |n(n^2+5)

    We need to show that 6 divides (n+1)((n+1)^2+5)

    (n+1)((n+1)^2+5)=n^3+3n^2+3n+1+5n+5

    Now grouping the terms like this we get

    (n^3+5n) + 6 +3n(n+1)

    The first group is divisible by 6 from the induction hypothsis 6 is obviously divisible by 6.

    Notice that for every integer n n(n+1) is even and so it can be written in the form 2k for some integer k.

    3n(n+1) =3 \cdot 2k=6k this is also divisible by 6.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Induction Proof - Divisibility
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: February 5th 2011, 09:32 PM
  2. Proof by Induction (Divisibility)
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 8th 2010, 02:30 PM
  3. Proof using principle of strong induction
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: September 20th 2010, 04:16 PM
  4. Principle of Induction Proof
    Posted in the Algebra Forum
    Replies: 9
    Last Post: October 14th 2008, 11:57 AM
  5. [SOLVED] Proof of divisibility by Induction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: November 14th 2007, 09:15 PM

Search Tags


/mathhelpforum @mathhelpforum