a: \(=5+\dfrac{1}{5}-\dfrac{2}{9}+\dfrac{2}{23}-\dfrac{3}{35}-\dfrac{5}{6}-8-\dfrac{2}{7}+\dfrac{1}{18}\)

\(=-3+\left(-\dfrac{2}{9}-\dfrac{5}{6}+\dfrac{1}{18}\right)+\left(\dfrac{1}{5}+\dfrac{2}{23}-\dfrac{3}{35}-\dfrac{2}{7}\right)\)

\(=-3+\dfrac{-12-45+1}{18}+\dfrac{7-10-3}{35}+\dfrac{2}{23}\)

\(=3-\dfrac{28}{9}+\dfrac{-6}{35}+\dfrac{2}{23}=\dfrac{-1417}{7245}\)

^{1/2 + 2/3 - 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 *...* 29/30 : 6/10}

^{= 1/2 + 2/3 - 1/10 : 6/10}

^{= 1/2 + 2/3 - 1/6}

^{= 1}

z là gì vậy bn

A ) \(=\dfrac{2\times9\times11\times2\times19\times2}{11\times19\times9}=\dfrac{8}{1}=8\)

b)\(=\dfrac{2}{5}\times\left(\dfrac{4}{7}+\dfrac{9}{7}+\dfrac{8}{7}\right)=\dfrac{2}{5}\times\dfrac{21}{7}=\dfrac{2}{5}\times3=\dfrac{6}{5}\)

Ta xét vế 1 : (27 x 45 + 27 x 55)

=27 x (45+55)

=27 x 100=2700

Vế 2 : 2+4+6+8+10+.....+18

Ta thấy đây là dãy số chẵn từ 2 đến 18

Số số hạng của dãy là :

(18-2):2+1=9

Tổng của dãy là ;

(18+2)x9:2=90

Ta lại có :2700 : 90 

=30

=27x(45+55): ((18+2)x9/2)

=2700:90

=30

=[27x(45+55)]:[(2+18)+(4+16)+(6+14)+(8+12)+10]

=[27x100]:[20+20+20+20+10]

=2700:90

=30

\(=\left(-\dfrac{1}{6}-\dfrac{5}{6}\right)+\left(\dfrac{25}{9}+\dfrac{2}{9}\right)=-1+3=2\)

Câu 6: Tính bằng cách hợp lí:

 25/9 - 1/6 + 4/18 -5/6 = (25/9+4/18)+(-1/6-5/6)

                                   =3-1

                                  =2

\(=\dfrac{25}{9}-\dfrac{1}{6}-\dfrac{2}{9}-\dfrac{5}{6}\\ =\left(\dfrac{25}{9}-\dfrac{2}{9}\right)+\left(\dfrac{5}{6}-\dfrac{1}{6}\right)\\ =\dfrac{23}{9}+\dfrac{2}{3}\\ =\dfrac{23+6}{9}=\dfrac{29}{9}\)

a)

Vì 2/9=6/27=8/36=12/54=16/72=18/81 nên:

2/9+6/27+8/36+12/54+16/72+18/81=

2/9+2/9+2/9+2/9+2/9+2/9=

2/9*6=

12/9=

4/3

Vậy 2/9+6/27+8/36+12/54+16/72+18/81=4/3

b)

Ta có:

1-2/5=3/5

1-2/7=5/7

1-2/9=7/9

...

1-2/99=97/99

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=

3/5*5/7*7/9*...*97/99=

(3*5*7*...*97)/(5*7*9*...*99)=

3/99=

1/33

Vậy (1-2/5)*(1-2/7)*(1-2/9)*...*(1-2/99)=1/33

c)

Gọi biểu thức 1/2+1/4+1/8+1/16+...+1/1024 là S,ta có:

S=1/2+1/4+1/8+1/16+...+1/1024

S*2=1+1/2+1/4+1/8+...+1/512

S*2-S=(1+1/2+1/4+1/8+...+1/512)-(1/2+1/4+1/8+1/16+...+1/1024)

S=1-1/1024

S=1023/1024

Vậy 1/2+1/4+1/8+1/16+...+1/1024=1023/1024

Cảm ơn bạn nhé!

\(=\left(9-8-...-2-1\right)\left(500\cdot9-500\cdot9\right)=0\)

0

\(S=\dfrac{3}{4}-\dfrac{1}{4}-\left(\dfrac{7}{3}-\dfrac{9}{2}\right)-\dfrac{5}{6}\)

\(=\left(\dfrac{3}{4}-\dfrac{1}{4}+\dfrac{18}{4}\right)-\left(\dfrac{14}{6}+\dfrac{5}{6}\right)\)

\(=\dfrac{20}{4}-\dfrac{19}{6}=\dfrac{11}{6}\)

\(S=\dfrac{3}{4}-0,25-\left[\dfrac{7}{3}+\left(\dfrac{-9}{2}\right)\right]-\dfrac{5}{6}\)

   \(=\dfrac{3}{4}-0,25 +\dfrac{13}{6}-\dfrac{5}{6}\)

   \(=\dfrac{11}{6}\)