x^2 +x^10 = a0+a1(x+1)+a2(x+2)^2 +.+a10(x+1)^10 求a9

问题描述:

x^2 +x^10 = a0+a1(x+1)+a2(x+2)^2 +.+a10(x+1)^10 求a9

令x=y-1
则(y-1)^2+(y-1)^10=a0+a1 y+a2 y+……a9 y^9+a10 y^10
a9y^9=10 y^9 (-1)=-10y^9
a9=-10