Question

[Trần Thị Hồng Ngọc]

Cho đa thức f(x)=

x⁹⁹-3000.x⁹⁸+3000.x⁹⁷ -3000.x⁹⁶+....-3000.x²

+3000.x-1

Answer 1

[Bùi nguyễn quỳnh anh]

ta có:3000=2009+1 \Rightarrow f(2009)=200999200999-3000.200998200998+3000.200997200997-3000.200996200996+...+3000.2009-1 =200999200999-(2009+1)200998200998+(2009+1).200997200997-(2009+1).200996200996+...+(2009+1).2009-1 =200999200999-(200999200999+200998200998)+(200998200998+200997200997)-(200997200997)+.200996200996)+...+(2009220092+2009)-1 =200999200999-200999200999-200998200998+200998200998+200997200997-200997200997-200996200996+...+2009220092+2009-1 =2009-1 =2008