2:

a: \(=\dfrac{1}{3}\left(-\dfrac{4}{5}-\dfrac{6}{5}\right)=-\dfrac{1}{3}\cdot2=-\dfrac{2}{3}\)

1:

\(A=7-\dfrac{3}{4}+\dfrac{1}{3}-6-\dfrac{5}{4}+\dfrac{4}{3}-5+\dfrac{7}{4}-\dfrac{5}{3}\)

\(=-4-\dfrac{1}{4}=-\dfrac{17}{4}\)

Bài 1:

\(A=\left(7-\dfrac{3}{4}+\dfrac{1}{3}\right)-\left(6+\dfrac{5}{4}-\dfrac{4}{3}\right)-\left(5-\dfrac{7}{4}+\dfrac{5}{3}\right)\)

\(A=7-\dfrac{3}{4}+\dfrac{1}{3}-6-\dfrac{5}{4}+\dfrac{4}{3}-5+\dfrac{7}{4}-\dfrac{5}{3}\)

\(A=\left(7-6-5\right)-\left(\dfrac{3}{4}+\dfrac{5}{4}-\dfrac{7}{4}\right)+\left(\dfrac{1}{3}+\dfrac{4}{3}-\dfrac{5}{3}\right)\)

\(A=-4-\dfrac{3+5-7}{4}+\dfrac{1+4-5}{3}\)

\(A=-4-\dfrac{1}{4}+\dfrac{0}{3}\)

\(A=-\dfrac{16}{4}-\dfrac{1}{4}+0\)

\(A=\dfrac{-16-1}{4}\)

\(A=-\dfrac{17}{4}\)

Bài 2:

\(\dfrac{1}{3}\cdot-\dfrac{4}{5}+\dfrac{1}{3}\cdot-\dfrac{6}{5}\)

\(=\dfrac{1}{3}\cdot\left(-\dfrac{4}{5}-\dfrac{6}{5}\right)\)

\(=\dfrac{1}{3}\cdot\dfrac{-4-6}{5}\)

\(=\dfrac{1}{3}\cdot\dfrac{-10}{5}\)

\(=\dfrac{1}{3}\cdot-2\)

\(=-\dfrac{2}{3}\)

đầy đủ phần ngoặc hay gì đó

\(\dfrac{11}{2}\): \(\dfrac{1}{4}\) \(\times\) \(\dfrac{5}{3}\)

= \(\dfrac{11}{2}\) \(\times\) \(\dfrac{4}{1}\) \(\times\) \(\dfrac{5}{3}\)

= 22 \(\times\) \(\dfrac{5}{3}\)

= \(\dfrac{110}{3}\)

\(\dfrac{5}{2}-\dfrac{1}{4}+\dfrac{5}{3}\)

= \(\dfrac{30}{12}-\dfrac{3}{12}+\dfrac{20}{12}\)

= \(\dfrac{7}{12}\) 

\(\dfrac{14}{5}\times\dfrac{2}{3}\)+ 5

= \(\dfrac{28}{15}\) + 5

= \(\dfrac{28}{15}\) + \(\dfrac{75}{15}\)

= \(\dfrac{103}{15}\)

A = 1 x 1000 - 999

A = 1000 - 999

A = 1

Từ số 1 đến số 1 thứ 1000 có số chữ số 1 là:

(1000 - 1) : 1 + 1 = 1000(số)

Tổng dãy là:

(1000 + 1) x 1000 : 2 = 500500

Hiệu là:

500500 - 999 = 499501

Bài 1: 

a, \(\dfrac{-x-2}{3}\) = - \(\dfrac{6}{7}\)

      - \(x\) - 2 = - \(\dfrac{18}{7}\)

         \(x\)      = - 2 + \(\dfrac{18}{7}\)

         \(x\)      = - \(\dfrac{4}{7}\)

Bài b,  \(\dfrac{4}{7-x}\) = \(\dfrac{1}{3}\)

            12 = 7 - \(x\)

            \(x\)  = 7 - 12 

            \(x\)  = -5 

Bài 2

A = (6 - \(\dfrac{2}{3}\) + \(\dfrac{1}{2}\)) - (5 + \(\dfrac{5}{3}\) - \(\dfrac{3}{2}\)) - (3 - \(\dfrac{7}{3}\) + \(\dfrac{5}{2}\))

A = 6 - \(\dfrac{2}{3}\) + \(\dfrac{1}{2}\) - 5 - \(\dfrac{5}{3}\) + \(\dfrac{3}{2}\) - 3 + \(\dfrac{7}{3}\)  - \(\dfrac{5}{2}\)

A = (6 - 5 - 3) + ( \(\dfrac{1}{2}\) + \(\dfrac{3}{2}\) - \(\dfrac{5}{2}\)) - (\(\dfrac{2}{3}\) + \(\dfrac{5}{3}\) - \(\dfrac{7}{3}\))

A = -2 + (2 - \(\dfrac{5}{2}\)) - 0

A = -2 + 2 - \(\dfrac{5}{2}\)

A = - \(\dfrac{5}{2}\)

\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{997.999}\)

\(\Leftrightarrow C=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{997.999}\right)\)

\(\Leftrightarrow C=\frac{5}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{997}-\frac{1}{999}\right)\)

\(\Leftrightarrow C=\frac{5}{2}\left(1-\frac{1}{999}\right)=\frac{5}{2}.\frac{998}{999}=\frac{2495}{999}=2\frac{497}{999}\)

\(A=\frac{2}{4}+\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+\frac{2}{208}\)

\(\Leftrightarrow A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)

\(\Leftrightarrow A=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)

\(\Leftrightarrow A=\frac{2}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)

\(\Leftrightarrow A=\frac{2}{3}\left(1-\frac{1}{16}\right)=\frac{2}{3}.\frac{15}{16}=\frac{5}{8}\)

C = 5/1x3 + 5/3x5 + 5/5x7 + ... + 5/997x999

C = 5 - 5/3 + 5/3 - 5/5 + 5/5 - 5/7 + ... + 5/997 - 5/999

C = 5 - 5/999

C = bạn tự tính nhé !

A = 2/4 + 2/28 + 2/70 + 2/130 + 2/208

A = 2/1x4 + 2/4x7 + 2/7x10 + 2/10x13 + 2/13x16

A = 2 - 2/4 + 2/4 - 2/7 + 2/7 - 2/10 + 2/10 - 2/13 + 2/13 - 2/16

A = 2 - 2/16

A = bạn tự tính nhé !

\(\frac{2C}{5}=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{97.99}\)

\(\frac{2C}{5}=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{99-97}{97.99}\)

\(\frac{2C}{5}=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)

\(\frac{2C}{5}=1-\frac{1}{99}=\frac{98}{99}\Rightarrow C=\frac{98.5}{99.2}=\frac{245}{99}\)

\(\frac{3A}{2}=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\)

\(\frac{3A}{2}=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+\frac{13-10}{10.13}+\frac{16-13}{13.16}\)

\(\frac{3A}{2}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\)

\(\frac{3A}{2}=1-\frac{1}{16}=\frac{15}{16}\Rightarrow A=\frac{15.2}{16.3}=\frac{5}{8}\)

cách 2:

a=\(6-\frac{2}{3}+\frac{1}{2}-5-\frac{5}{3}+\frac{3}{2}-3+\frac{7}{3}-\frac{5}{2}\)

a=(6-5-3)-(2/3+5/3-7/3)+(1/2+3/2-5/2)

a=-2-1/2

a=-5/2

Cach 1 jdujsoidfojaiuh

 k cho mk nha !

Thay x=2005 vào biểu thức, ta được:

2005²⁰⁰⁵-2006*2005²⁰⁰⁴+...+2006*2005²-2006*2005-1

=2005²⁰⁰⁵-(2006*2005²⁰⁰⁴-..-2006*2005²+2006*2005+1)

Đặt A=(2006*2005²⁰⁰⁴-..-2006*2005²+2006*2005+1)

2005A=2006*2005²⁰⁰⁵-..-2006*2005³+2006*2005²+2005

2005A+2005*2006=2006*2005²⁰⁰⁵-..-2006*2005³+2006*2005²+2006*2005+1+2004=A+2004

2005A-A=2004-2005*2006

2004A=2004-2005*2006

A=(2004-2005*2006)/2004=1-(2005*2006)/2004

=>2005²⁰⁰⁵-(2006*2005²⁰⁰⁴-..-2006*2005²+2006*2005+1)=2005²⁰⁰⁵-1+(2005*2006)/2004

đến đây cậu làm được chưa, quy đồng lên rồi tính, phân phối ra ý