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

=>2S=\(\frac{2+2^2+...+2^{2009}}{1-2^{2009}}\)

=>2S-S=\(\frac{2+2^2+...+2^{2009}-1-2-2^2-...-2^{2008}}{1-2^{2009}}\)

S=\(\frac{2^{2009}-1}{1-2^{2009}}\)

=>S= -1

=>1/4:(x-2/3)=2

=>(x-2/3)=1/8

=>x=1/8+2/3=3/24+16/24=19/24

13/4 - 1/4 : ( x - 2/3 )= 5/4

\(\Rightarrow\) 1/4 : ( x- 2/3 ) = 13/4 - 5/4

\(\Rightarrow\) 1/4 : ( x- 2/3)= 2

\(\Rightarrow\) x - 2/3 = 1/4 :2

\(\Rightarrow\) x- 2/3 = 1/8

\(\Rightarrow\) x= 1/8 +2/3 =19/24

Vậy x = 19/24

\(\dfrac{13}{4}-\dfrac{1}{4}\div\left(x-\dfrac{2}{3}\right)=\dfrac{5}{4}\\ \Rightarrow\dfrac{1}{4}\div\left(x-\dfrac{2}{3}\right)=\dfrac{13}{4}-\dfrac{5}{4}\\ \Rightarrow\dfrac{1}{4}\div\left(x-\dfrac{2}{3}\right)=\dfrac{8}{4}=2\\ \Rightarrow x-\dfrac{2}{3}=\dfrac{1}{4}\div2\\ \Rightarrow x-\dfrac{2}{3}=\dfrac{1}{4}\times\dfrac{1}{2}\\ \Rightarrow x-\dfrac{2}{3}=\dfrac{1}{8}\\ \Rightarrow x-\dfrac{16}{24}=\dfrac{3}{24}\\ \Rightarrow x=\dfrac{3}{24}+\dfrac{16}{24}\\ \Rightarrow x=\dfrac{19}{24}\)

Vậy \(x=\dfrac{19}{24}\) 

(1-2)+(3-4)+...+(2011-2012).........(có (2012-1+1):2=1006 cặp số)

=-1+-1+-1+.......+-1

=-1.1006=-1006

tick nha

a)

`9/2-3`

`=9/2-6/2`

`=3/2`

b)

`8/5xx25/12`

`=10/3`

c)

`4:3/7`

`=4xx7/3`

`=28/3`

thank you bạn

    A = 8 - 8² + 8 + 8³ + 8⁴+ ......+ 8⁹⁹

        A = ( 8 - 8 ) + ( 8² + 8³ + 8⁴ +......+ 8⁹⁹ )

        A = 8² + 8³ + 8⁴ +......+ 8⁹⁹

       8A = 8³ + 8⁴ + 8⁵ +.......+ 8¹⁰⁰ 

  8A - A = ( 8³ + 8⁴ +...+ 8¹⁰⁰ ) - ( 8² + 8³ + ...+ 8⁹⁹ )

       7A = 8¹⁰⁰ - 8²

    => A = \(\frac{8^{100}-8^2}{7}\)

VẬY, \(A=\frac{8^{100}-8^2}{7}\)

cho A=8+8^2+8^3+..+8^299+8^300.  CHỨNG MINH RẰNG 7A+8 LÀ LŨY THỪA CỦA 8

gio con noc ha ?!

<=> 2x^2 +x-4x-2-5x-15=2x^2-6x+4+8x-2-2x

      2x^2-8x-17-2x^2-2=0

     -8x-19=0

x=-19/8

(x-2).(2x+1)-5(x+3)=2x(x-3)+4(1+2x)-2(1+x)

3x-4x+x-2-5x-15=3x-6x+4+8x-2-2x

-5x-17=3x+2

-19=8x

-19/8=x

Vậy x=-19/8