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Thread: Prove inequalities

  1. #1
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    Unhappy Prove inequalities

    Prove that 4^n > 7n^2 for n > 3
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  2. #2
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    Re: Prove inequalities

    Quote Originally Posted by raggie29 View Post
    Prove that 4^n > 7n^2 for n > 3
    Is it true for $\displaystyle n= 3~?$

    If $\displaystyle k>3$ and it is true that $\displaystyle 4^k\ge 7k^2$ does it follow that
    $\displaystyle 4^{k+1}\ge 7(k+1)^2~?$
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  3. #3
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    Re: Prove inequalities

    Yes it is true for n=3 since, 4^n =64 and 7n^2 = 63

    So yes it does followe the k+1 example is this correct?
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  4. #4
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    Re: Prove inequalities

    Yes, that is "proof by induction". If a statement, depending on n, is true when n= 3, and, whenever it is true for n= k, it is also true that n= k+1.
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