问题 选择题
lim
n→∞
Cn2n
Cn+12n+2
=(  )
A.0B.2C.
1
2
D.
1
4
答案

Cn2n
=
(2n)!
n!(2n-n)!
Cn+12n+2
=
(2n+2)!
(n+1)!(n+1)!

Cn2n
Cn+12n+2
=
(2n)!
n!n1
×
(n+1)!(n+1)!
(2n+2)!
=
(n+1)(n+1)
(2n+2)(2n+1)
=
n2+2n+1
4n2+6n+2

lim
n→∞
Cn2n
Cn+12n+2
=
lim
n→∞
n2+2n+1
4n2+6n+2
=
1
4

故选D.

单项选择题
单项选择题