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Thread: Mathematical Induction

  1. March 23rd 2010, 05:03 PM #1
    MATNTRNG
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    Mathematical Induction

    Prove using mathematical induction:

    49|(2^(3n) - 7n - 1)
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  2. March 23rd 2010, 07:56 PM #2
    tonio
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    Quote Originally Posted by MATNTRNG View Post
    Prove using mathematical induction:


    49|(2^(3n) - 7n - 1)

    Check for n = 1 and complete the explanation in the following:

    2^{3(n+1)}-7(n+1)-1=8\cdot 2^{3n}-7n-7-1=\left(2^{3n}-7n-1\right)+7\cdot 2^{3n}-7= 49k+7\left(2^{3n}-1\right)=49k+7(2^3-1)(2^{3(n-1)}+2^{3(n-2)}+\ldots+2^3+1) , k\in\mathbb{N}

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