How to prove the inequality $\frac{4^m}{4\sqrt{m}}\le\binom{2m}{m}$ using chebyshev inequality

Asked Dec 28 '16 at 10:07

Active Dec 28 '16 at 11:27

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What is a good approach to proving this inequality:

$$\dfrac{4^m}{4\sqrt{m}}\le\binom{2m}{m}$$

I thought about using a random variable which has a binomial distribution, but im not sure.

Thank you!

EDIT: It is important to solve it only using Chebychev inequality

edited Dec 28 '16 at 11:27

asked Dec 28 '16 at 10:07

user3720340

thank you, but this answer is not using chebyshev... – user3720340 Dec 28 '16 at 10:50
It is, but there are different Chebyshev inequalities, e.g. this one, or this one. Which one do you mean? – Dietrich Burde Dec 28 '16 at 10:57
the second. thanks! – user3720340 Dec 28 '16 at 11:26

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