Question

证明(2*4*6*8*...2n)/(1*3*5*7*...(2n-1)>根号(2n+1)

Answer 1

设Y=(2*4*6*8*...2n)/(1*3*5*7*...(2n-1)

那么Y^2=[(2*4*6*8*...2n)/(1*3*5*7*...(2n-1))]^2

而

2^2>1*3

4^2>3*5

.

(2n)^2>(2n-1)(2n+1)

于是分子>1*3^2*5^2*7^2*.*(2n+1)

所以Y^2>2n+1

Y>根号(2n+1)