a)\(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{91.94}+\frac{2}{94.97}\)

=\(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{91}-\frac{1}{94}+\frac{1}{94}-\frac{1}{97}\)(giản ước các phân số giống nhau)

=\(\frac{1}{1}-\frac{1}{97}\)

=\(\frac{96}{97}\)

a)    gọi \(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.11}+...+\frac{2}{94.97}\)

               \(\Rightarrow\frac{3}{2}A=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{94.97}\)

                     \(\frac{3}{2}A=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{94}-\frac{1}{97}\)(rút gọn các phân số giống nhau)

                      \(\frac{3}{2}A=\frac{1}{1}-\frac{1}{97}\)

                       \(\frac{3}{2}A=\frac{96}{97}\left(1\right)\)

                       từ \(\left(1\right)\Leftrightarrow A=\frac{96}{97}\div\frac{3}{2}=\frac{64}{97}\)

b)\(\left(1-\frac{1}{7}\right).\left(1-\frac{1}{8}\right).\left(1-\frac{1}{9}\right).....\left(1-\frac{1}{2011}\right)\)

    \(=\frac{6}{7}.\frac{7}{8}.\frac{8}{9}......\frac{2010}{2011}\)

 \(=\frac{6.7.8.9.....2010}{7.8.9......2011}\)(rút gọn các số giống nhau)

\(=\frac{6}{2011}\)

Câu a Nguyễn Triệu Yến Nhi đúng

Cậu b bao quynh Cao đúng

\(-\frac{2000}{139}\)

A=\(\frac{-41000}{973}\)

giup minh vs

Đặt : \(A=\frac{\left[13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right]\cdot230\frac{1}{25}+46\frac{3}{4}}{\left[1\frac{3}{10}+\frac{10}{3}\right]:\left[12\frac{1}{3}-14\frac{2}{7}\right]}\)

\(A=\frac{\left[\frac{53}{4}-\frac{59}{27}-\frac{65}{6}\right]\cdot\frac{5751}{25}+\frac{187}{4}}{\left[\frac{13}{10}+\frac{10}{3}\right]:\left[\frac{37}{3}-\frac{100}{7}\right]}\)

\(A=\frac{\left[\frac{1431}{108}-\frac{236}{108}-\frac{1170}{108}\right]\cdot\frac{5751}{25}+\frac{187}{4}}{\left[\frac{39}{30}+\frac{100}{30}\right]:\left[\frac{259}{21}-\frac{300}{21}\right]}\)

\(A=\frac{\frac{25}{108}\cdot\frac{5751}{25}+\frac{187}{4}}{\frac{139}{30}:\left[-\frac{41}{21}\right]}\)

\(A=\frac{\frac{5751}{108}+\frac{187}{4}}{\frac{139}{30}\cdot\left[-\frac{21}{41}\right]}\)

\(A=\frac{\frac{5751}{108}+\frac{5049}{108}}{-\frac{973}{410}}=\frac{100}{-\frac{973}{410}}=-\frac{41000}{973}\)

thank you huynh quang sang