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Math Help - Proof by Induction with Inequalities

  1. #1
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    Exclamation Proof by Induction with Inequalities

    I'm having a lot of trouble with the induction step of the following proof. I really just don't even know how to start manipulating the inequality. Any help would be appreciated. Thanks.

    Show that (n+1)(n-1) ≤ nn for all n>0.
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  2. #2
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    Re: Proof by Induction with Inequalities

    Make the statement that you assume \displaystyle \begin{align*} \left( k + 1 \right) ^{k - 1} \leq k^k \end{align*}, then using this assumption, try to show that \displaystyle \begin{align*} \left( k + 2 \right) ^k \leq \left( k + 1 \right) ^{k + 1} \end{align*}.
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    Re: Proof by Induction with Inequalities

    I understand the process of a proof by induction, but I'm having trouble manipulating the n=k case to show that the n=k+1 case is true as well.
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  4. #4
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    Re: Proof by Induction with Inequalities

    Use this: a^b = a*a^(b-1)
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