biểu thức gì zậy bn?

\(\frac{1}{19}+\frac{9}{19.29}+\frac{9}{29.39}+....+\frac{9}{1999.2009}\)

=\(\frac{1}{19}+\frac{1}{10}.\left(\frac{9}{19}-\frac{9}{29}+\frac{9}{29}-\frac{9}{39}+....+\frac{9}{1999}-\frac{9}{2009}\right)\)

=\(\frac{1}{19}+\frac{1}{10}.\left(\frac{9}{19}-\frac{9}{2009}\right)\)

=\(\frac{1}{19}+\frac{1791}{38171}\)

=\(\frac{200}{2009}\)

Ghi cái quần què gì thế

Ta có :

\(A=\dfrac{1}{2^2}+\dfrac{1}{2^3}+.................+\dfrac{1}{9^2}\)

Xét :

\(\dfrac{1}{2^2}< \dfrac{1}{1.2}\)

\(\dfrac{1}{2^3}< \dfrac{1}{2.3}\)

..................................

\(\dfrac{1}{9^2}< \dfrac{1}{8.9}\)

\(\Rightarrow A< \dfrac{1}{1.2}+\dfrac{1}{2.3}+...............+\dfrac{1}{8.9}\)

\(\Rightarrow A< \dfrac{1}{1}-\dfrac{1}{9}=\dfrac{8}{9}\)

\(\Rightarrow A< \dfrac{8}{9}\rightarrowđpcm\) \(\left(1\right)\)

Xét :

\(\dfrac{1}{2^2}>\dfrac{1}{2.3}\)

\(\dfrac{1}{2^3}>\dfrac{1}{3.4}\)

......................

\(\dfrac{1}{9^2}>\dfrac{1}{9.10}\)

\(\Rightarrow A>\dfrac{1}{2.3}+\dfrac{1}{3.4}+.............+\dfrac{1}{9.10}\)

\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{10}\)

\(\Rightarrow A>\dfrac{2}{5}\rightarrowđpcm\)\(\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Rightarrow\dfrac{8}{9}>A>\dfrac{2}{5}\rightarrowđpcm\)

~ Chúc bn học tốt ~

a,

đoạn 9x-6-> 2x-6=0

=> x=3

b,6x^2+13x+5=6x^2-20x+6

33x=1

=>x=1/33

a) (x+1)(x+9)=(x+3)(x+5) 

<=>x^2+10x+9=x^2+8x+15

<=>x^2+10x+9-x^2-8x-15=0

<=>9x-6=0 phải là 2x - 6

<=>9x=6

<=>x=6/9=2/3 => S= 2/3

d) (3x+5)(2x+1)=(6x-2)(x-3)

<=>6x^2+13x+5=6x^2-16x+6 phải là 6x^2 - 20x + 6

<=>6x^2+13x+5-6x^2+16x-6=0

<=>29x-1=0

<=>29x=1

<=>x=1/29

Ta có:\(A< \frac{1}{1.2}+\frac{1}{2.3}+......+\frac{1}{8.9}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}=1-\frac{1}{9}=\frac{8}{9}\)

Mặt khác:\(A>\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{9.10}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{9}-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{4}{10}=\frac{2}{5}\)

Vậy \(\frac{8}{9}>A>\frac{2}{5}\)

 Bạn Bảo Bình đúng rồi 

ta xét vế trái =1+\(\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}\)=\(\frac{2}{ab}+1\)

mặt khác :a+b>=\(2\sqrt{ab}\)

=> (a+b)^2>=4ab

=>ab<=\(\frac{1}{4}\)

=>1/ab>=1/4

=>VT>=1+2*4=9

dấu = khi a=b=1/2

a) x - 3 = -6 => x = ( -6 ) + 3 => x = -3

b) x - ( -5 ) = 4 => x = 4 + ( -5 ) => x = -1

c) x - ( -9 ) = 4 - ( -9 ) => x = 4

d) 4 - x = -3 - ( -6 ) => x = 4 - [ ( -3 ) - ( -6 ) ] => x = 1

 720 : ( x . 2 + x . 3 ) = 3.2
720 : ( x . 2 + x.3 ) = 6
( x .2 + x.3 )           = 720 : 6 
x.2+x.3 = 120
x . ( 2 + 3 ) = 120
x . 5 = 120
     x     = 120 : 5 
    x      = 24