Question

若(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

Answer 1

∵（x+1）⁵=[2+（x-1）]⁵=

C

05

•2⁵+

C

15

•2⁴（x-1）+

C

25

•2³•（x-1）²+

C

35

•2²（x-1）³+

C

45

•2•（X-1）⁴+

C

55

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

C

55

•2⁵=32，
故选B．