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A level inequalities/proof math question

Example 6.14
Let n be a positive integer.

Prove that
[br]2n−1/2n[br]{2n-1}/{2n} < 2n−12n+1[br] \sqrt{\frac {2n-1}{2n+1}}[br]

from hong kong a level
(edited 8 years ago)
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Spandy
3
Notice that 2n-1 is always >1. Thus, you just have to show that {sqrt.(2n-1)}/2n < 1/{sqrt.(2n+1)}
It effectively implies that we have to show that {sqrt.([4n^2]-1)} < 2n.
(Sorry, never bothered to take Latex seriously)
Original post by CancerousProblem
Example 6.14
Let n be a positive integer.

Prove that
[br]2n−1/2n[br]{2n-1}/{2n} < 2n−12n+1[br] \sqrt{\frac {2n-1}{2n+1}}[br]

from hong kong a level


Do you want to know how to do it? Or a general Problem?


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