Question

3x^2+10x^10=a0+a1(x-1)+a2(x-1)^2+.+a9(x-1)^9+a10(x-1)^10 求a9

Answer 1

由题目可知：

左侧：x^10的系数项是a10(说明a10=10)

x^9的系数项是a9 + 10*a10*（-1）（关键理解后面一项 应该有10个a10项）

理由如下：a10(x-1)^10=a10(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)(x-1)

=a10（x^10+10*x^9*（-1）+10*x^8*（-1）*（-1）+.

所以a9 + 10*a10*（-1）=0

a9=100