\(...=\dfrac{3}{2}x\dfrac{4}{3}x\dfrac{5}{4}x\dfrac{6}{5}x\dfrac{7}{6}....x\dfrac{1000}{999}\)

\(=\dfrac{1}{2}x\dfrac{1000}{1}=500\)

=3/2x4/3x5/4x....x1000/999

=1/2x1000=500

mình chưa chắc là đúng đâu nhé

\(1\dfrac{1}{3}\times1\dfrac{1}{8}\times1\dfrac{1}{15}\times1\dfrac{1}{24}\times1\dfrac{1}{35}\)

= \(\dfrac{4}{3}\times\dfrac{9}{8}\times\dfrac{16}{15}\times\dfrac{25}{24}\times\dfrac{36}{35}\)

= \(\dfrac{4\times9\times16\times25\times36}{3\times8\times15\times24\times35}\)

= \(\dfrac{1\times2\times2\times25\times36}{1\times2\times15\times24\times35}\)

= \(\dfrac{4\times25\times36}{30\times24\times35}\)

= \(\dfrac{1\times25\times36}{30\times6\times35}=\dfrac{1}{7}\)

\(1\dfrac{1}{3}\times1\dfrac{1}{8}\times1\dfrac{1}{15}\times1\dfrac{1}{24}\times1\dfrac{1}{35}\)

\(=\dfrac{4}{3}\times\dfrac{9}{8}\times\dfrac{16}{15}\times\dfrac{25}{24}\times\dfrac{36}{35}\)

\(=\dfrac{2\times2}{1\times3}\times\dfrac{3\times3}{2\times4}\times\dfrac{4\times4}{3\times5}\times\dfrac{5\times5}{4\times6}\times\dfrac{6\times6}{5\times7}\)

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

\(=6\times\dfrac{2}{7}=\dfrac{12}{7}\)

`1:(1 1/2 xx 1 1/3 xx 1 1/4 xx ... xx 1 1/99 )`

`= 1 : (3/2 xx 4/3 xx 5/4 xx ... xx 100/99)`

`= 1 : 100/2`

`= 1 xx 2/100`

`= 2/100`

`=1/50`

\(=>C=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}.....\cdot\dfrac{101}{100}\)

\(C=\dfrac{3\cdot4\cdot5.......\cdot101}{2\cdot3\cdot4.........\cdot100}\)

\(C=\dfrac{101}{2}\)

\(C=1\dfrac{1}{2}\cdot1\dfrac{1}{3}\cdot1\dfrac{1}{4}\cdot...\cdot1\dfrac{1}{100}\)

\(C=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{101}{100}\)

\(C=\dfrac{101}{2}\)

a: \(1\dfrac{1}{2}\cdot1\dfrac{1}{3}\cdot1\dfrac{1}{4}\)
\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\)

\(=\dfrac{5}{2}\)

b: \(1\dfrac{1}{2}:1\dfrac{1}{3}:1\dfrac{1}{4}\)

\(=\dfrac{3}{2}:\dfrac{4}{3}:\dfrac{5}{4}\)

\(=\dfrac{3}{2}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}=\dfrac{9}{10}\)

x = nhân nhé

\(=\dfrac{4}{5}+\dfrac{2}{3}x.\dfrac{55}{4}=\dfrac{4}{5}+\dfrac{55}{6}x\)

      1\(\dfrac{1}{12}\) \(\times\) 1\(\dfrac{1}{13}\) \(\times\) 1\(\dfrac{1}{14}\) \(\times\)...\(\times\)1\(\dfrac{1}{2005}\)

A = \(\dfrac{12+1}{12}\) \(\times\) \(\dfrac{13+1}{13}\) \(\times\) \(\dfrac{14+1}{14}\)\(\times\)...\(\times\) \(\dfrac{2006}{2005}\)

A = \(\dfrac{13}{12}\) \(\times\) \(\dfrac{14}{13}\) \(\times\) \(\dfrac{15}{14}\) \(\times\)...\(\times\) \(\dfrac{2006}{2005}\)

A = \(\dfrac{2006}{12}\)

A = \(\dfrac{1003}{6}\)

` a/`

` 2 - 1 5/6 + 2 2/3 = 2 - 11/6 - 8/3 = 1/6+ 8/3 = 1/6 + 16/6 = 17/6 `

`b/`

`5/9 xx ( 2 5/6 - 1 2/3 ) = 5/9 xx ( 17/6 - 5/3 ) = 5/9 xx 7/6 = 35/54 `

`c/`

` 1 1/3 : ( 2 + 1 1/6 : 2 5/6 ) `

`= 4/3 :  ( 2 + 7/6 : 17/6 ) `

`= 4/3 : ( 2 + 7/6 xx 6/17 )`

`= 4/3 : ( 2 + 7/17 ) `

`= 4/3 : ( 34/17 + 7/17 ) `

`= 4/3 : 41/17 `

`= 4/3 xx 17/41 `

`= 68/123`

` d/` 

` 2 3/5 : 3/4 xx 1 4/5 = 13/5 xx 4/3 xx 9/5 =52/15 xx 9/5 = 156/25`

a: A=x1+x2=-5/2

b: \(=\dfrac{x_1+x_2}{x_1x_2}=\dfrac{-5}{2}:\left(-1\right)=\dfrac{5}{2}\)

c: \(=\left(x_1+x_2\right)^3-3x_1x_2\left(x_1+x_2\right)\)

\(=\left(-\dfrac{5}{2}\right)^3-3\cdot\dfrac{-5}{2}\cdot\left(-1\right)\)

\(=-\dfrac{125}{8}-\dfrac{15}{2}=\dfrac{-185}{8}\)

e: \(E=\sqrt{\left(x_1+x_2\right)^2-4x_1x_2}\)

\(=\sqrt{\left(-\dfrac{5}{2}\right)^2-4\cdot\left(-1\right)}=\sqrt{\dfrac{25}{4}+4}=\dfrac{\sqrt{41}}{2}\)