Question

lim

n→∞

(1+2+22+…+2n)2

C 12n + C 32n +…+ C 2n-12n

等于（　　）

A．16

B．8

C．4

D．2

Answer 1

lim

n→∞

(1+2+22+…+2n)2

C 12n + C 32n +…+ C 2n-12n

=

lim

n→∞

[ 1×(1-2n) 2 ]2

22n-1

=

lim

n→∞

(2n-1)2

22n-1

=

lim

n→∞

22n-2•2n+1

22n-1

=2；
故选D．