Question

lim

n→∞

C 0n + C 1n + C 2n

1+3+5+…+(2n-1)

=（　　）

A．1

B． 1 2

C． 1 3

D． 1 4

Answer 1

∵

C

0n

+

C

1n

+

C

2n

=1+n+

1

2

n(n-1)=

1

2

 n2+

1

2

n+1
1+3+5+…+（2n-1）=

1+2n-1

2

•n=n²
∴

lim

n→∞

C 0n + C 1n + C 2n

1+3+5+…+(2n-1)

=

lim

n→∞

1 2 (n2+n+2)

n2

=

lim

n→∞

(

1

2

+

1

2n

+

1

n2

 )=

1

2

故选B