Prove that for all sufficiently large n,

$\displaystyle \frac{(1+\log2)n}{\log\frac{n}{2}} \leq \frac{2n}{\log n}$

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- Mar 19th 2013, 06:02 PMKanwar245Proving inequality
Prove that for all sufficiently large n,

$\displaystyle \frac{(1+\log2)n}{\log\frac{n}{2}} \leq \frac{2n}{\log n}$ - Mar 19th 2013, 08:29 PMProve ItRe: 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.

- Mar 19th 2013, 08:29 PMprincepsRe: Proving inequality
First , find by guessing some small value for which inequality holds , then prove inequality using math induction .

- Mar 19th 2013, 08:30 PMchiroRe: 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). - Mar 19th 2013, 08:31 PMProve ItRe: Proving inequality
- Mar 19th 2013, 08:38 PMprincepsRe: Proving inequality
- Mar 20th 2013, 11:32 AMKanwar245Re: Proving inequality
- Mar 20th 2013, 03:30 PMProve ItRe: Proving inequality