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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
    Cheers
    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

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    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
     
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