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Math Help - Proving inequality

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    Junior Member Kanwar245's Avatar
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    Proving inequality

    Prove that for all sufficiently large n,

    \frac{(1+\log2)n}{\log\frac{n}{2}} \leq \frac{2n}{\log n}
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    Re: Proving inequality

    Well for starters, find the smallest value where the inequality holds true, then show the right hand function grows faster than the left hand function.
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    Re: Proving inequality

    First , find by guessing some small value for which inequality holds , then prove inequality using math induction .
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    Re: Proving inequality

    Hey Kanwar245.

    Hint: Try taking log(n/2) to the RHS and use the fact that log(n/2) = log(n) - log(2).
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    Re: Proving inequality

    Quote Originally Posted by princeps View Post
    First , find by guessing some small value for which inequality holds , then prove inequality using math induction .
    Is mathematical induction wise here? We aren't told that n only takes on integer values...
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    Re: Proving inequality

    Quote Originally Posted by Prove It View Post
    Is mathematical induction wise here? We aren't told that n only takes on integer values...
    Common notation for integer variable is a letter "n" .
    Last edited by princeps; March 19th 2013 at 08:43 PM.
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    Re: Proving inequality

    Quote Originally Posted by Prove It View Post
    Well for starters, find the smallest value where the inequality holds true, then show the right hand function grows faster than the left hand function.
    How can I show that the function on the right side grows faster than the function on the left side?
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    Re: Proving inequality

    Quote Originally Posted by Kanwar245 View Post
    How can I show that the function on the right side grows faster than the function on the left side?
    Take the derivative of each side. Show the right hand derivative is greater than the left.
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