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(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x.......x (1-1/2003)x(1-1/2004)
=1/2 x 2/3 x 3/4 x 4/5 x.....x2002/2003 x 2003/2004
=\(\frac{1\times2\times3\times4\times...\times2002\times2003}{2\times3\times4\times5....\times2003\times2004}\)
=\(\frac{1}{2004}\)
\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x...x\left(1-\frac{1}{2003}\right)x\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{2002}{2003}x\frac{2003}{2004}\)
\(=\frac{1x2x3x4x....x2002x2003}{2x3x4x5x...x2003x2004}\)
\(=\frac{1}{2004}\)
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
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{2002}{2003}.\frac{2003}{2004}\)
\(=\frac{1.2.3...2002.2003}{2.3.4...2003.2004}=\frac{1}{2004}\)
\(\frac{1}{2}.x-\frac{3}{4}=\frac{5}{6}\)
\(\frac{1}{2}.x=\frac{5}{6}+\frac{3}{4}\)
\(\frac{1}{2}.x=\frac{10}{12}+\frac{9}{12}=\frac{19}{12}\)
\(x=\frac{19}{12}:\frac{1}{2}\)
\(x=\frac{19}{12}.2=\frac{19}{6}\)
\(B=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times...\times\left(1-\frac{1}{2004}\right)\)
\(=\left(\frac{2}{2}-\frac{1}{2}\right)\times\left(\frac{3}{3}-\frac{1}{3}\right)\times...\times\left(\frac{2003}{2003}-\frac{1}{2003}\right)\times\left(\frac{2004}{2004}-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)
\(=\frac{1\times2\times...\times2002\times2003}{2\times3\times...\times2003\times2004}\)
\(=\frac{1}{2004}\)
=> B = 1/2 * 2/3 * 3/4 * 4/5 *...* 2002/2003 * 2003/2004 = 1/2004
\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot....\cdot\frac{2003}{2004}\)
\(=\frac{1\cdot2\cdot....\cdot2003}{2\cdot3\cdot....\cdot2004}\)
\(=\frac{1}{2004}\)
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
A = ( 6 : 3/5 - 7/6 * 6/7 ) : ( 21/5 * 10/11 + 57/11 )
A = ( 10 - 1 ) : ( 42/11 + 57/11)
A = 9 : 9
A = 1
B = 59 /10 : 3/2 - ( 7/3 * 9/2 - 2 * 7/3 ) : 7/4
B = 59/15 - ( 21/2 - 14/3 ) : 7/4
B = 59/15 - 35/6 : 7/4
B = 59/15 - 10/3
B = 3/5
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)
=\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}......\frac{2012}{2013}.\frac{2013}{2014}\)
=\(\frac{1}{2014}\)
Đề bài
= \(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)
= \(1\times2\times3\times4\times...\times2002\times2003/2\times3\times4\times5\times...2003\times2004\)
= \(\frac{1}{2004}\)
Đề bài
= 1/2 x 2/3 x 3/4 x 4/5 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 5 x .... x 2003 x 2004
= 1/2004
K nha