Question

若(1-2x)^5=a0+a1(x-1)+a2（x-1）^2+.+a5（x-1）^5,

Answer 1

(1-2x)^5=a0+a1(x-1)+a2(x-1)^2+.+a5(x-1)^5

则设f(x)=(1-2x)^5

求导数得：

f'(x)=5[(1-2x)^4]*(-2)=-10(1-2x)^4

且f'(x)=a1+2a2(x-1)+3a3(x-1)^2+4a4(x-1)^3+5a5(x-1)^4

令x=2

则：(1-2*2)^4=a1+2a2+3a3+4a4+5a5

即：a1+2a2+3a3+4a4+5a5

=(-3)^4

=81