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1 tháng 8 2020

\(\frac{10}{11}:\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(=\frac{10}{11}:\left(\frac{11}{33}-\frac{3}{33}\right)\)

\(=\frac{10}{11}:\frac{8}{33}\)

\(=\frac{15}{4}\)

Học tốt

1 tháng 8 2020

\(\frac{10}{11}:\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(=\frac{10}{11}:\frac{8}{33}\)

\(=\frac{10}{11}.\frac{33}{8}\)

\(=\frac{15}{4}\)

31 tháng 7 2020

\(\frac{10}{11}:\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(=\frac{10}{11}:\frac{8}{33}=\frac{10}{11}.\frac{33}{8}\)

\(=\frac{15}{4}\)

31 tháng 7 2020

Trả lời:

\(\frac{10}{11}\div\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)

\(=\frac{10}{11}\div\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{10}{11}\div\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(=\frac{10}{11}\div\frac{8}{33}\)

\(=\frac{10}{11}\times\frac{33}{8}\)

\(=\frac{15}{4}\)

26 tháng 9 2020

\(\frac{33}{2}+\frac{33}{6}+\frac{33}{18}+\frac{33}{54}+\frac{33}{162}+\frac{33}{486}\)

\(=\frac{33.3+33.3+33.3+33.3+33.3}{486}\)

\(=\frac{99.5}{486}\)

\(=\frac{495}{486}\)

26 tháng 9 2020

Gọi \(A=\frac{33}{2}+\frac{33}{6}+...+\frac{33}{486}\)

\(A=33.\left[\left(\frac{1}{1.2}+\frac{1}{2.3}\right)+\left(\frac{1}{3.6}+\frac{1}{6.9}\right)\left(\frac{1}{9.18}+\frac{1}{18.27}\right)\right]\)

\(A=33.\left[\frac{2}{3}+\frac{2}{9}+\frac{2}{27}\right]\)

\(A=66.\left[\frac{9}{27}+\frac{3}{27}+\frac{1}{27}\right]\)

\(A=66.\frac{13}{27}\)

\(A=\frac{286}{9}\)

sai hay đúng cx ko biết nha

6 tháng 8 2016

\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)

\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)

\(=\frac{1}{1.3}-\frac{1}{11.13}\)

\(=\frac{1}{3}-\frac{1}{143}\)

\(=\frac{140}{429}\)

8 tháng 7 2018

\(\frac{4}{3.5}-\frac{6}{5.7}+\frac{8}{7.9}+\frac{10}{9.11}+...+\frac{2016}{2015.2017}\)

\(=2.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)

\(=2.\left(\frac{1}{3}-\frac{1}{2017}\right)\)

\(=2.\frac{2014}{6051}\)

\(=\frac{4028}{6051}\)

\(\Rightarrow BT>\frac{1}{6}\)

9 tháng 10 2020

\(A=\frac{4}{3\cdot5}+\frac{4}{5\cdot7}+\frac{4}{7\cdot9}+\frac{4}{9\cdot11}\)

\(A=\frac{2\cdot2}{3\cdot5}+\frac{2\cdot2}{5\cdot7}+\frac{2\cdot2}{7\cdot9}+\frac{2\cdot2}{9\cdot11}\)

\(A=2\cdot\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\right)\)

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

\(A=2\cdot\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(A=2\cdot\frac{8}{33}\)

\(A=\frac{16}{33}\)

9 tháng 10 2020

Ta có: 

\(A=\frac{4}{3.5}+\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}\)

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

\(A=2\left(\frac{1}{3}-\frac{1}{11}\right)\)

\(A=2\cdot\frac{8}{33}\)

\(A=\frac{16}{33}\)

31 tháng 3 2017

a) \(C=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)

       \(=7\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\)

       \(=7\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right)\)

       \(=7\left(\frac{1}{2}-\frac{1}{28}\right)\)

       \(=7.\frac{13}{28}=\frac{7.13}{28}=\frac{13}{4}\)

b) \(B=\frac{6}{3.5}+\frac{6}{5.7}+\frac{6}{7.9}+...+\frac{6}{97.99}\)

      \(=3\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\right)\)

      \(=3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)

       \(=3\left(\frac{1}{3}-\frac{1}{99}\right)\)

       \(=3.\frac{32}{99}=\frac{3.32}{99}=\frac{32}{33}\)

1 tháng 4 2017

mình cũng làm như trên