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Math Help - Proving Inequalities with exponents by means of MI.

  1. #1
    Junior Member Kaloda's Avatar
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    Proving Inequalities with exponents by means of MI.

    Using mathematical induction, prove that for all integers n\geq3,
    (n+1)^n<n^{n+1}.
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  2. #2
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    Re: Proving Inequalities with exponents by means of MI.

    Quote Originally Posted by Kaloda View Post
    Using mathematical induction, prove that for all integers n\geq3,
    (n+1)^n<n^{n+1}.
    What is the first step in this proof? You can at least do that.
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  3. #3
    Junior Member Kaloda's Avatar
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    Re: Proving Inequalities with exponents by means of MI.

    Quote Originally Posted by Plato View Post
    What is the first step in this proof? You can at least do that.
    Haha. Of course I do. I'm good in proving equality statements, i.e. sequence and summations,
    using mathematical induction but not inequalities like this one.

    What I did was I assumed that k^{k-1}<(k-1)^k and then I tried to prove (k+1)^k<k^{k+1}.
    After that, I really have no idea what to do next. Please help. TY.
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