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10 tháng 4 2017

10/21 nha bạn

10 tháng 4 2017

\(=\frac{181}{385}\)

10 tháng 4 2017

1/1.3+1/3+5+1/5.7+...+1/19.21

=1/2(2/1.3+2/3.5+2/5.7+...+2/19.21

=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/19-1/21)

=1/2(1-1/21)

=1/2.20/21

=10/21

10 tháng 4 2017

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{5}-\frac{1}{5}+\frac{1}{7}-\frac{1}{7}+....-\frac{1}{19}+\frac{1}{21}-\frac{1}{21}\)\(\frac{1}{21}\)

\(=\frac{1}{1}-\frac{1}{21}\)

\(=\frac{21}{21}-\frac{1}{21}\)

\(=\frac{20}{21}\)

10 tháng 4 2017

Đặt A = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\)

2A = \(2.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\right)\)

2A = \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\)

2A = \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)

2A = \(1-\frac{1}{21}\)

2A = \(\frac{21}{21}-\frac{1}{21}\)

2A = \(\frac{20}{21}\)

=> A = \(\frac{20}{21}:2\)

A = \(\frac{20}{21}.\frac{1}{2}\)

A = \(\frac{20}{42}\)

A = \(\frac{10}{21}\)

Vậy \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}=\frac{10}{21}\)

10 tháng 4 2017

\(\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+...+\frac{1}{19x21}\)

\(=\frac{1}{2}x\left(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{19x21}\right)\)

\(=\frac{1}{2}x\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)

\(=\frac{1}{2}x\left(1-\frac{1}{21}\right)\)

\(=\frac{1}{2}x\frac{20}{21}\)

\(=\frac{10}{21}\)

10 tháng 4 2017

thanks everyone

10 tháng 4 2017

\(\frac{10}{12}\)nha bạn

9 tháng 8 2015

a) = 17/19 - 17/19 + 27/35 + 35/35 = 0 + 62/35

b) = 1/3 x 4/5 + 1/3 x6/5 + 1/3 x 2 = 1/3(4/5 + 6/5 + 2) = 1/3 x 4 = = 4/3

c) 4/7 x 2/9 + 4/7 x 7/9 + 2/3 = 4/7 x (2/9 + 7/9) + 2/3 = 4/7 x 1 + 2/3 = 26/21

4 tháng 3 2022

A) 17/19 - 17/19 + 27/35 + 35/35 = 0 + 62/35

B) 1/3 x 4/5 + 1/3 x 6/5 + 1/3 x 2 = 1/3 x(4/5 + 6/5 x 2 ) = 1/3 x 4 = 4/3

c) TƯƠNG TỰ CÂU A VÀ B

* HOKTOT*

NHA

10 tháng 6 2015

1> a) \(\frac{5}{7}x4:\frac{5}{9}=\frac{5}{7}:\frac{5}{9}x4=\frac{5}{7}x\frac{9}{5}x4=\frac{9}{7}x4=\frac{9x4}{7}=\frac{36}{7}\)

\(b,8x\frac{2}{3}:\frac{1}{2}=8x\frac{2}{3}x\frac{2}{1}=8x2x\frac{2}{3}=16x\frac{2}{3}=\frac{32}{3}\)

\(c,6:\frac{3}{5}-\frac{7}{6}x\frac{6}{7}=6x\frac{5}{3}-1=10-1=9\)

\(\frac{21}{5}x\frac{10}{11}+\frac{57}{11}=\frac{42}{11}+\frac{57}{11}=\frac{99}{11}=9\)

2) a) \(\frac{35}{9}:x=\frac{35}{6}\)

\(x=\frac{35}{9}:\frac{35}{6}\)

\(x=\frac{35}{9}x\frac{6}{35}\)

\(x=\frac{2}{3}\)

b) \(\left(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\right)x10-X=0\)

\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{5}-\frac{1}{6}\right)x10-X=0\)

\(\left(\frac{1}{1}-\frac{1}{6}\right)x10-X=10\)

\(\frac{5}{6}x10-X=0\)

\(X=\frac{5}{6}x10=\frac{25}{3}\)

Đúng nha !!!!

10 tháng 6 2015

1/a/\(\frac{5}{7}\cdot4:\frac{5}{9}=\frac{20}{7}:\frac{5}{9}=\frac{20}{7}\cdot\frac{9}{5}=\frac{36}{7}\)

b/\(8\cdot\frac{2}{3}:\frac{1}{2}=\frac{16}{3}:\frac{1}{2}=\frac{16}{3}\cdot\frac{2}{1}=\frac{32}{3}\)

c/\(6:\frac{3}{5}-\frac{7}{6}\cdot\frac{6}{7}=6\cdot\frac{5}{3}-1=10-1=9\)

2/a/\(\frac{35}{9}:x=\frac{35}{6}\)

\(x=\frac{35}{9}:\frac{35}{6}=\frac{35}{9}\cdot\frac{6}{35}\)

\(x=\frac{2}{3}\)

 

b/\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\right)\cdot10-x=0\)

\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\cdot10-x=0\)

\(\left(\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{2}{30}\right)\cdot10-x=0\)

\(\frac{47}{60}\cdot10-x=0\)

\(\frac{47}{6}-x=0\)

\(x=\frac{47}{6}-0\)

\(x=\frac{47}{6}\)