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Math Help - Math Induction

  1. #1
    MHF Contributor
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    Math Induction

    Use mathematical induction to prove: 3 is a factor of
    n^3 + 2n

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  2. #2
    MHF Contributor
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    Hello

    Let P(n) be the property "3 is a factor of n^3+2n"

    1^3+2\:\: 1\;=\;3 therefore P(1) is true

    Let's suppose P(n) true and demonstrate that P(n+1) is true

    (n+1)^3+2(n+1)\;=\;n^3+3n^2+3n+1+2n+2
    (n+1)^3+2(n+1)\;=\;n^3+2n+3n^2+3n+3
    (n+1)^3+2(n+1)\;=\;(n^3+2n)+3(n^2+n+1)

    P(n) supposed true => 3 is a factor of n^3+2n
    3 is clearly a factor of 3(n^2+n+1)

    Therefore 3 is a factor of (n^3+2n)+3(n^2+n+1)
    P(n+1) is true
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