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11 tháng 9 2022

2 phép tính trên không có khó 

\(\left(1-\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}\right)\cdot....\cdot\left(1-\dfrac{1}{2003}\right)\cdot\left(1-\dfrac{1}{2004}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot....\cdot\dfrac{2002}{2003}\cdot\dfrac{2003}{2004}\)

\(=\dfrac{1\cdot2\cdot3\cdot....\cdot2002\cdot2003}{2\cdot3\cdot4\cdot....\cdot2003\cdot2004}\)

\(=\dfrac{1}{2004}\)

14 tháng 6 2023

a) \(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2003}\right).\left(1-\dfrac{1}{2004}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}...\dfrac{2002}{2003}.\dfrac{2003}{2004}\)

\(=\dfrac{1}{2004}\)

b) \(B=5\dfrac{9}{10}:\dfrac{3}{2}-\left(2\dfrac{1}{3}.4\dfrac{1}{2}-2.2\dfrac{1}{3}\right):\dfrac{7}{4}\)

\(=\dfrac{59}{10}:\dfrac{3}{2}-\left(\dfrac{7}{3}.\dfrac{9}{2}-2.\dfrac{7}{3}\right).\dfrac{4}{7}\)

\(=\dfrac{59}{15}-\left(\dfrac{21}{2}-\dfrac{14}{3}\right).\dfrac{4}{7}\)

\(=\dfrac{59}{15}-\dfrac{35}{6}.\dfrac{4}{7}\)

\(=\dfrac{59}{15}-\dfrac{10}{3}\)

\(=\dfrac{3}{5}\)

14 tháng 6 2023

ai trả lời đúng thì mình sẽ tick cho

13 tháng 8 2016

1) =1/2 x 2/3 x 3/4 x 4/5 x .... x 2002/2003 x 2003/2004

=1/2004

2) 1/2 x X-3/4=5/6

1/2 x X =3/4+5/6

1/2 x X =19/12

X=19/6

13 tháng 8 2016

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2002}{2003}.\frac{2003}{2004}\)

\(=\frac{1.2.3...2002.2003}{2.3.4...2003.2004}=\frac{1}{2004}\)

\(\frac{1}{2}.x-\frac{3}{4}=\frac{5}{6}\)

\(\frac{1}{2}.x=\frac{5}{6}+\frac{3}{4}\)

\(\frac{1}{2}.x=\frac{10}{12}+\frac{9}{12}=\frac{19}{12}\)

\(x=\frac{19}{12}:\frac{1}{2}\)

\(x=\frac{19}{12}.2=\frac{19}{6}\)

13 tháng 8 2017

Giúp mình nhanh nha! Mình sẽ thick người đó

6 tháng 8 2023

\(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2003}\right).\left(1-\dfrac{1}{2004}\right)\)

\(A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}....\dfrac{2002}{2003}.\dfrac{2003}{2004}\)

\(A=\dfrac{1}{2004}\)

9 tháng 8 2023

\(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2004}\right)\)

\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2003}{2004}\)

\(B=\dfrac{1\cdot2\cdot3\cdot...\cdot2003}{2\cdot3\cdot4\cdot...\cdot2004}\)

\(B=\dfrac{1}{2004}\)

9 tháng 8 2023

B=(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)...(1-1/2003)x(1-1/2004)

B=1/2x2/3x3/4x4/5x...x2002/2003x2003/2004

B=1/2004

TH
Thầy Hùng Olm
Manager VIP
14 tháng 7 2023

\(B=\dfrac{1}{2}x\dfrac{2}{3}x\dfrac{3}{4}x...x\dfrac{2003}{2004}\)

\(B=\dfrac{1}{2004}\)

14 tháng 7 2023

\(B=\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times....\left(1-\dfrac{1}{2003}\right)\times\left(1-\dfrac{1}{2004}\right)\)

\(B=\dfrac{1}{2}\times\dfrac{2}{3}\times....\times\dfrac{2002}{2003}\times\dfrac{2003}{2004}\) 

\(B=\dfrac{1}{2004}\)

24 tháng 8 2017

B= 1/2 x 2/3 x 3/4 x ...........x 2002/2003 x 2003/2004

1 x 2 x 3 x 4 x .............x 2002 x 2003

2 x 3 x 4 x .............x 2003 x 2004

1

 2004

12 tháng 5 2016

bn ơi 1/3 ko đc bn ơi

18 tháng 8 2023

\(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2003}\right).\left(1-\dfrac{1}{2004}\right).\)

\(\Rightarrow A=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}....\dfrac{2002}{2003}.\dfrac{2003}{2004}\)

\(\Rightarrow A=\dfrac{1}{2004}\)

HQ
Hà Quang Minh
Giáo viên
18 tháng 8 2023

\(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)...\left(1-\dfrac{1}{2004}\right)\\ =\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}...\dfrac{2003}{2004}\\ =\dfrac{1}{2004}\)