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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
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2002}{2003}.\frac{2003}{2004}\)
\(=\frac{1.2.3...2002.2003}{2.3.4...2003.2004}=\frac{1}{2004}\)
\(\frac{1}{2}.x-\frac{3}{4}=\frac{5}{6}\)
\(\frac{1}{2}.x=\frac{5}{6}+\frac{3}{4}\)
\(\frac{1}{2}.x=\frac{10}{12}+\frac{9}{12}=\frac{19}{12}\)
\(x=\frac{19}{12}:\frac{1}{2}\)
\(x=\frac{19}{12}.2=\frac{19}{6}\)
\(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2004}\right)\)
\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2003}{2004}\)
\(B=\dfrac{1\cdot2\cdot3\cdot...\cdot2003}{2\cdot3\cdot4\cdot...\cdot2004}\)
\(B=\dfrac{1}{2004}\)
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
\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{5}\right)\cdot....\cdot\left(1-\frac{1}{2003}\right)\cdot\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot....\cdot\frac{2002}{2003}\cdot\frac{2003}{2004}\)
\(=\frac{1\cdot2\cdot3\cdot4\cdot....\cdot2002\cdot2003}{2\cdot3\cdot4\cdot5\cdot....\cdot2003\cdot2004}\)
\(=\frac{1}{2004}\)
\(A=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{2002}{2003}x\frac{2003}{2004}\)
\(A=\frac{1x\left(2x3x4x...x2002x2003\right)}{\left(2x3x4x...x2002x2003\right)x2004}=\frac{1}{2004}\)
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)
=\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{2012}{2013}.\frac{2013}{2014}\)
=\(\frac{1}{2014}\)
ta sẽ ra được kết quả qua cách giảm ước của cả tử và mẫu . vậy cuối cùng nhìn lại trên tử còn 1 mẫu thì còn 2004 vậy phân số ra được là 1/2004
B = \(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x........x\left(1-\frac{1}{2003}\right)x\left(1-\frac{1}{2004}\right)\)
B = \(\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x.........x\frac{2002}{2003}x\frac{2003}{2004}\)
=> B = \(\frac{1}{2004}\)
\(B=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2003}\right)\times\left(1-\frac{1}{2004}\right)\)
\(B=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)
\(B=\frac{1\times2\times3\times...\times2002\times2003}{2\times3\times4\times...\times2003\times2004}\)
\(\Rightarrow B=\frac{1}{2004}\)
bn ơi 1/3 ko đc bn ơi