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Math Help - Prove x^n > x for all x > 1.

  1. #16
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    Quote Originally Posted by lvleph View Post
    Yes, because the hint was to prove f(x) > g(x) and we wanted to prove x^n > x so it makes sense to assume g(x)=x.

    how about I do this

    Factorise! x^n-x=x(x^{n-1}-1)=x(x-1)(1+x+x^2+\cdots+x^{n-2}), the product of three terms which are obviously positive for x\,>\,1.

    does this make sense?
    Last edited by Jameson; November 24th 2009 at 03:20 PM.
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  2. #17
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    Yes, and it's way better.
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