tự làm là hạnh phúc của mỗi công dân.

Thiếu đề : Tính f(2009)

\(F\left(x\right)=x^{98}-\left(x+1\right)x^{97}+\left(x+1\right)x^{96}+...-\left(x+1\right)x^2+\left(x+1\right)x-1\)

\(=x^{98}-x^{98}-x^{97}+x^{97}+x^{96}-x^{96}...-x^3-x^2+x^2+x-1\)

\(=x-1=2009-1=2008\)

3000 :2=?

Ta có : 

(x + 1) + (x + 3) + (x + 5) + ... + (x + 99) = 3000

(x + x + x + ... + x) + (1 + 3 + 5 + 99) = 3000

50x + 2500 = 3000

50x = 3000 - 2500

50x = 500

x = 500 : 50

x = 10

Vậy x = 10

Ủng hộ mk nha !!! ^_^

( x + 1 ) + ( x + 3 ) + ( x + 5 ) + ... + ( x + 99 ) =3000

x + ( 1  +3 + 5 + ... + 99 ) = 3000

x + 2500 = 3000

x = 3000 - 2500

x = 500

Chúc bạn học tốt!

Đây là toán 4 chứ ko phải toán 6

( x + 1 ) + ( x + 3 ) + ( x + 5 ) + ... + ( x + 99 ) =3000

x + ( 1  +3 + 5 + ... + 99 ) = 3000

x + 2500 = 3000

x = 3000 - 2500

x = 500

đặt 3000=x+1 ta đc

F(x)=\(x^{98}-\left(x+1\right)x^{97}+\left(x+1\right)x^{96}+...-\left(x+1\right)x^2+\left(x+1\right)x-1=x^{98}-x^{98}-x^{97}+x^{97}+x^{96}-x^{96}.....-x^3-x^2+x^2+x-1=x-1=2009-1=2008\)

vậy.......

f(x)=x⁹⁹-3000.x⁹⁸+3000.x⁹⁷-...-3000x²+3000x-1

f(2009)=x⁹⁹-(x+1).x⁹⁸+(x+1).x⁹⁷-...-(x+1)x²+(x+1)x-1

=x⁹⁹-x⁹⁹-x⁹⁸+x⁹⁸+x⁹⁷-...-x³-x²+x²+x-1

=(x⁹⁹-x⁹⁹)+(-x⁹⁸+x⁹⁸)+(x⁹⁷-x⁹⁷)...+(-x²+x²)+x-1

=2009-1

=2008

f(x)=x99-3000.x98+3000.x97-...-3000x2+3000x-1

f(2009)=x99-(x+1).x98+(x+1).x97-...-(x+1)x2+(x+1)x-1

=x99-x99-x98+x98+x97-...-x3-x2+x2+x-1

=(x99-x99)+(-x98+x98)+(x97-x97)...+(-x2+x2)+x-1

=2009-1

=2008

Ta có : 2999=x => x⁹⁹-3000x⁹⁸⁺3000x⁹⁷-...+3000x-1

f(x) = x⁹⁹ - (x+1)x⁹⁸+(x+1)x⁹⁷-...+(x+1)x-1

=x⁹⁹-x⁹⁹-x⁹⁸+x⁹⁸+x⁹⁷-...x²+x-1=x-1=2999-1=2998

Vậy : f(2999)= 2998

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