问题 填空题

(x+1)5=a0+a1(x-1)+a2(x-1)2+…+a5(x-1)5,则a0=(  )

A.1

B.32

C.-1

D.-32

答案

∵(x+1)5=[2+(x-1)]5=

C05
•25+
C15
•24(x-1)+
C25
•23•(x-1)2+
C35
•22(x-1)3+
C45
•2•(X-1)4+
C55
•(x-1)5

而且 (x+1)5=a0+a1(x-1)+a2(x-1)2+…+a5(x-1)5

故 a0=

C55
•25=32,

故选B.

单项选择题
填空题