3/2*5/4*7/6*9/8*...2n+1/2n>根号下n+1?怎么证明?
问题描述：
3/2*5/4*7/6*9/8*...2n+1/2n>根号下n+1?怎么证明?
答
数学归纳法
答
（3/2*5/4*7/6*9/8*...2n+1/2n）²
=（3/2*5/4*7/6*9/8*...2n+1/2n）（3/2*5/4*7/6*9/8*...2n+1/2n）
>(3/2*5/4*7/6*9/8*...2n+1/2n)(4/3*6/5*8/7*10/9...(2n+2)(2n+1))
=(2n+2)/2=n+1
∴ 3/2*5/4*7/6*9/8*...2n+1/2n>√(n+1)