ko trả lời gì mà cũng đc tick sao, hay nhỉ

x=0,5         

a, \(\frac{1}{2009}+\frac{2}{2009}+...+\frac{2008}{2009}\\ \frac{\left(1+2008\right)\cdot2008\div2}{2009}=\frac{2017036}{2009}\)

Dễ quá, thực hiện qui tắc bỏ dấu ngoặc được:

 \(2009+2009^2+....+2009^{2009}-1-2009-...-2009^{2008}\)

\(=-1+\left(2009-2009\right)+\left(2009^2-2009^2\right)+...+\left(2009^{2008}-2009^{2008}\right)+2009^{2008}\)

\(=2009^{2008}-1\)

\(=\left(2009-1\right)\left(2009^{2007}+2009^{2008}+...+2009+1\right)\)

\(=2008\left(2009^{2007}+2009^{2008}+...+2009+1\right)\) chia hết cho 2008

=> ĐPCM

Chứng Minh Rằng: (2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁹)-(1+2009+2009²+2009³+...+2009²⁰⁰⁸) chia hết cho 2008.

Đặt A=2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁹, B=1+2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁸

Ta có:

+)A=2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁹

  2009A= 2009²+2009³+2009⁴+...+2009²⁰¹⁰

   2009A-A=(2009²+2009³+2009⁴+...+2009²⁰¹⁰)-(2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁹)

  2008A=2009²⁰¹⁰- 2009

=> A=(2009²⁰¹⁰- 2009)/2008 

=> A chia hết cho 2008.

B=1+2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁸

2009B=2009+2009²+2009³+2009⁴+...+2009²⁰¹⁰

2009B-B=(2009+2009²+2009³+2009⁴+...+2009²⁰¹⁰)-(1+2009+2009²+2009³+2009⁴+...+2009²⁰⁰⁹)

2008B=2009²⁰¹⁰-1

=>B=(2009²⁰¹⁰-1)/2008

=>B chia hết cho 2008

=> A-B chia hết cho 2008.

=> ĐPCM

2008×(2009-84)+1004×(-32-2×2009)

=>2008×1925+1004×-4050

=>3865400+-4066200

=-200800

Chúc bạn học tốt!

=-200800

-200800

=2008/2009-2009/2008+1/2009+2007/2008

=(2008/2009+1/2009)-(2009/2008-2007/2008)

=1-1/1004

=1003/1004

\(\frac{2008}{2009}-\frac{2009}{2008}+\frac{1}{2009}+\frac{2007}{2008}\)

=\(\left(\frac{2008}{2009}+\frac{1}{2009}\right)-\left(\frac{2009}{2008}-\frac{2007}{2008}\right)\)

=\(1-\frac{2}{2008}\)

=\(1-\frac{1}{1004}\)

=\(\frac{1003}{1004}\)

Chúc bn làm tốt nha!!!