(-1)^n*n!
泰勒展开:
f(x)=f(0)+f'(0)x+[f''(0)/2]x^2+.
f(0)=0.
等式两边除以x:
f(x)/x=f'(0)+[f''(0)/2]x+.
令x=0:
(x-1)(x-2)...(x-n)=f'(0)
f'(0)=(-1)^n*n!
(-1)^n*n!
泰勒展开:
f(x)=f(0)+f'(0)x+[f''(0)/2]x^2+.
f(0)=0.
等式两边除以x:
f(x)/x=f'(0)+[f''(0)/2]x+.
令x=0:
(x-1)(x-2)...(x-n)=f'(0)
f'(0)=(-1)^n*n!