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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(B=\dfrac{1\cdot2\cdot3\cdot4\cdot5\cdot...\cdot2003}{2\cdot3\cdot4\cdot5\cdot...\cdot2004}\)

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

L = 1/2 x 2/3 x 3/4 x ... X 2003/2004.rút gọn biểu thứ ta được 1/2004.

từng cách một nhé bạn

Ta có \(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2021}\right)\left(1-\dfrac{1}{2022}\right)\)

\(B=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{2020}{2021}.\dfrac{2021}{2022}\)

\(B=\dfrac{1}{2022}\)

giúp mik với ạ

B = (1 - \(\dfrac{1}{2}\))(1 - \(\dfrac{1}{3}\))(1 - \(\dfrac{1}{4}\))...(1-\(\dfrac{1}{2021}\))(1 - \(\dfrac{1}{2022}\))

B = \(\dfrac{2-1}{2}\)\(\times\)\(\dfrac{3-1}{3}\)\(\times\)\(\dfrac{4-1}{4}\)\(\times\)...\(\times\)\(\dfrac{2021-1}{2021}\)\(\times\)\(\dfrac{2022-1}{2022}\)

B = \(\dfrac{1}{2}\)\(\times\)\(\dfrac{2}{3}\)\(\times\)\(\dfrac{3}{4}\)\(\times\)...\(\times\)\(\dfrac{2020}{2021}\)\(\times\)\(\dfrac{2021}{2022}\)

B = \(\dfrac{2\times3\times4\times...\times2021}{2\times3\times4\times...\times2021}\) \(\times\) \(\dfrac{1}{2022}\)

B = \(\dfrac{1}{2022}\)

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

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

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

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

B = 1/2004