Bạn xem lời giải của mình nhé:

Giải:

\(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{93.95}\\ =\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{93}-\frac{1}{95}\\ \frac{1}{5}-\frac{1}{95}\\ =\frac{19-1}{95}=\frac{18}{95}\)

Chúc bạn học tốt!

Ta thấy: \(\frac{2}{5.7}=\frac{1}{5}-\frac{1}{7};\frac{2}{7.9}=\frac{1}{7}-\frac{1}{9};.....;\frac{2}{93.95}=\frac{1}{93}-\frac{1}{95}\)

\(S=\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{93.95}\)

\(S=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-.....-\frac{1}{95}\)

\(S=\frac{1}{5}-\frac{1}{95}=\frac{18}{95}\)

Ta có

B= 2×(1/5×7+1/7×9+1/9×11+...+1/93×95)

B= 2/2 ×( 1/5-1/7 + 1/7 - 1/9 +1/9 - 1/11 +...+1/93+1/93 -1/95)

B=2/2× (1/5 - 1/95)

B= 2/2× 18/95

B= 18/95

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

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

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

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

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

Trả lời:

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

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

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

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

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

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

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

=\(\frac{10}{11}:(\frac{2}{3}-\frac{2}{5}+\frac{2}{5}-\frac{2}{7}+\frac{2}{7}-\frac{2}{9}+\frac{2}{9}-\frac{2}{11})\)

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

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

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

= \(\frac{10}{11}.\frac{33}{8}\)= \(\frac{15}{4}\)

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

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

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

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

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

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

Học tốt

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

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

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

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

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

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

\(\frac{10}{11}:\left(\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\right)\)

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

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

\(=\frac{10}{11}:\frac{8}{33}=\frac{15}{4}\)

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

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

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

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

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

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

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

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

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

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

\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\)

\(=1+\frac{2}{3}-\frac{2}{3}+\frac{2}{5}-\frac{2}{5}+....+\frac{2}{15}\)

\(=1+\frac{2}{15}\)

\(=\frac{17}{15}\)

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

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

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

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

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

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

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

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

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

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

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

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

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

Ta có: 

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

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

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

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

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