Question

设(2-x)^5=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5,则a1+a3+a5=?

Answer 1

(2-x)^5=a0+a1x+a2x^2+a3x^3+a4x^4+a5x^5

令x=1

1 = a0+a1+a2+a3+a4+a5(1)

令x=-1

3^5 = a0-a1+a2-a3+a4-a5(2)

(1)-(2)得

1-3^5 = 2(a1+a3+a5)

a1+a3+a5 = (1/2)[1-3^5]