问题 选择题
lim
n→∞
C22
+
C23
+
C24
+…+
C2n
n(
C12
+
C13
+
C14
+…+
C1n
)
等于(  )
A.3B.
1
3
C.
1
6
D.6
答案

∵C22+C32+C42+…+Cn2=C33+C32+C42++Cn2=C43+C42+…+Cn2═Cn+13

n(

C12
+
C13
+
C14
++
C1n
)=n
(2+n)(n-1)
2

lim
n→∞
C22
+
C23
+
C24
++
C2n
n(
C12
+
C13
+
C14
++
C1n
)
=
lim
n→∞
C3n+1
n(n-1)(n+2)
2
=
lim
n→∞
(n+1)n(n-1)
6
n(n-1)(n+2)
2
=
1
3

故选B.

单项选择题
单项选择题