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Math Help - Mathematical Induction proving

  1. #1
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    Mathematical Induction proving

     n^{3}+2n


    prove that it is divisible by 3 for any integer   n\geq 1
    the steps i use are
    1) plug in a number to see if its true 1+2 = 3 is divisible by 3= true
    2). K=N plug it in  k^{3}+2k
    3) K+1 =N plug it in  k^{3}+2k+ (k+1)^{3} +2(k+1)  ---- this is where I'm confused i usually have numbers for example 1+3+4+5+.......(3n+2) = n(n+1)
    I'm not sure if step 3 is right because that's what i do for my usual example with numbers
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Mathematical Induction proving

    Hint: add (n+1)^3+2(n+1)-(n^3+2n)=3(n^2+n+1) to your induction hypothesis.
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  3. #3
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    Re: Mathematical Induction proving

    Same thing:
    (n+1)^3+ 2(n+1)= n^3+ 3n^2+ 3n+ 1+ 2n+ 2= (n^3+ 2n)+ (3n^2+ 3n+ 3)= (n^3+2n)+ 3(n^2+ n+ 1).
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