Question

我只会用二项式定理拆开,如果也是拆公式通项的就算了.

Answer 1

对 (1+2x)^4=a(0)+a(1)x+a(2)x²+a(3)x³+a(4)x^4 两边求导,得

8(1+2x)³=a(1)+2a(2)x+3a(3)x²+4a(4)x³

令x=-1,则

8(1-2)³=-8=a(1)-2a(2)+3a(3)-4a(4)

即 a(1)-2a(2)+3a(3)-4a(4)=-8