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29 tháng 3 2019

\(\left(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+\frac{1}{9x11}\right)xX=\frac{8}{11}\)

\(\Rightarrow\left(\frac{2}{3x5}+\frac{2}{5x7}+\frac{2}{7x9}+\frac{2}{9x11}\right)xX=\frac{16}{11}\)

\(\Rightarrow\left(\frac{5-3}{3x5}+\frac{7-5}{5x7}+\frac{9-7}{7x9}+\frac{11-9}{9x11}\right)xX=\frac{16}{11}\)

\(\Rightarrow\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)xX=\frac{16}{11}\)

\(\Rightarrow\left(\frac{1}{3}-\frac{1}{11}\right)xX=\frac{16}{11}\Rightarrow\frac{8}{33}xX=\frac{16}{11}\)

\(\Rightarrow X=\frac{16}{11}:\frac{8}{33}=\frac{16}{11}x\frac{33}{8}=6\)

29 tháng 3 2019

Theo đề bài

\(\overline{abc,d}-\overline{a,bcd}=583,704\)

\(\Rightarrow100x\overline{a,bcd}-\overline{a,bcd}=583,704\)

\(\Rightarrow99x\overline{a,bcd}=583,704\Rightarrow\overline{a,bcd}=583,704:99=5,896\Rightarrow\overline{abc,d}=589,6\)

Tổng hai số là

\(\overline{589,6}+5,896=595,496\)

31 tháng 5 2018

\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+\frac{1}{9x11}+\frac{1}{11x13}\)

\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{1}{2}x\left(\frac{1}{3}-\frac{1}{13}\right)\)

\(=\frac{1}{2}x\frac{10}{39}\)

\(=\frac{5}{39}\)

31 tháng 5 2018

\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\)

\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{13}\right)\)

\(=\frac{1}{2}\cdot\frac{10}{39}=\frac{5}{39}\)

1/1 x 3 + 1/3 x 5 + 1/5 x 7 + 1/7 x 9 + 1/9 x 11

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11

= 1 - 1/11

= 10/11

18 tháng 8 2015

\(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{9.11}=\frac{1}{2}\left(\frac{2}{1.3}+\frac{1}{3.5}+....+\frac{2}{9.11}\right)\)

\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....-\frac{1}{11}\right)=\frac{1}{2}.\left(1-\frac{1}{11}\right)\)

\(=\frac{1}{2}.\frac{10}{11}=\frac{5}{11}\)

28 tháng 10 2019

Tính thuận tiện

Ta có : 

\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)

\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)

\(\frac{1}{1}-\frac{1}{11}\)

\(\frac{10}{11}\)

DD
7 tháng 11 2021

\(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+\frac{1}{11\times13}\)

\(=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+\frac{2}{11\times13}\right)\)

\(=\frac{1}{2}\times\left(\frac{3-1}{1\times3}+\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+\frac{9-7}{7\times9}+\frac{11-9}{9\times11}+\frac{13-11}{11\times13}\right)\)

\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=\frac{1}{2}\times\left(1-\frac{1}{13}\right)=\frac{6}{13}\)

Do đó ta có: 

\(\frac{6}{13}\times y=\frac{3}{5}\)

\(\Leftrightarrow y=\frac{13}{10}\).

27 tháng 3 2022

ngu các em học quá ngu

9 tháng 6 2018

\((\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11})\cdot y=\frac{2}{3}\)

\(\Rightarrow(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11})\cdot y=\frac{2}{3}\)

\(\Rightarrow1-\frac{1}{11}\cdot y=\frac{2}{3}\)

\(\Rightarrow\frac{10}{11}\cdot y=\frac{2}{3}\)

\(\Rightarrow y=\frac{2}{3}:\frac{10}{11}=\frac{11}{15}\)

Vậy :\(y=\frac{11}{15}\)

Bạn có muốn mình thử lại không?

10 tháng 6 2018

không cảm ơn bạn

8 tháng 7 2016

\(=\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{9.11}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{11}\right)\)

\(=\frac{1}{2}.\frac{10}{11}\)

\(=\frac{5}{11}\)

8 tháng 7 2016

\(=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+....+\frac{2}{9\times11}\right)\)

\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{1}{2}\times\left(1-\frac{1}{11}\right)\)

\(=\frac{1}{2}\times\frac{10}{11}\)

\(=\frac{5}{11}\)