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Mathematical induction

  1. Oct 17, 2007 #1
    1. The problem statement, all variables and given/known data

    n [tex]\epsilon[/tex][tex]N[/tex]=n[tex]\geq0[/tex]
    6 divides (n[tex]^{3}[/tex]+5n)

    2. Relevant equations
    (n[tex]^{3}[/tex]+5n)=6q


    3. The attempt at a solution
    by expanding and simplifying and later on substituting 6q in
    (n+1)[tex]^{}3[/tex]+5(n+1)

    ive arrived at 6q+3n[tex]^{}2[/tex] +3n+6

    then.. im stuck...pls help...lot of thanks!
     
  2. jcsd
  3. Oct 17, 2007 #2
    i tried multiplying and dividing it by two so that the 6 would be factored out...ive got fractions..its supposed to be whole numbers
     
  4. Oct 18, 2007 #3
    (n+1)^3 +5(n+1)
    n^3 + 3n^2 + 3n + 1 + 5n + 5
    (n^3 + 5n) + 3n^2 + 3n + 6
    6q + 3n^2 + 3n + 6
    This reduces the problem down to proving that 3n^2 + 3n + 6 is a multiple of 6

    3(n^2 + n + 2)
    Now you just have to prove that n^2 + n + 2 is a multiple of 2, (is even).
     
    Last edited: Oct 18, 2007
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