Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof by induction

  1. May 21, 2009 #1
    Use mathematical induction, to prove that [tex]\frac{n^{3}+5n}{3}[/tex]

    is an even integer for each natural number n.

    I am fimilar with proof by induction but in most of the question that I have done have a
    LHS = RHS which seems to simplifiy things a little bit.
    Any help would be appreciated
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. May 21, 2009 #2

    Shooting Star

    User Avatar
    Homework Helper

    Put n+1 in place of n.

    (n+1)^3 + 5(n+1) = n^3+3n^2+3n+1+5n+5 = (n^3+5n) + 3n(n+1) + 6.

    Now divide each term by 3 and see what kind of number you get.

    Since you are familiar with induction, this should be enough.
  4. May 21, 2009 #3
    Got it thanks mate
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Proof by induction
  1. Proof by induction (Replies: 2)

  2. Proof by induction (Replies: 9)

  3. Proof by induction (Replies: 32)

  4. Induction Proof (Replies: 14)

  5. Proof by Induction (Replies: 6)