ko hiểu cái quy luật của nó

Ta có:\(\frac{1}{2.9}=\frac{1}{2}-\frac{1}{9}\)

\(\frac{1}{9.7}=\frac{1}{9}-\frac{1}{7}\)

\(⋮\)

\(\frac{1}{252.504}=\frac{1}{252}-\frac{1}{504}\)

\(A=\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{7}+\frac{1}{7}-...............+\frac{1}{252}-\frac{1}{504}\)

\(A=\frac{1}{2}-\frac{1}{504}\)

\(A=\frac{251}{504}\)

\(\frac{101}{1018}\)

B= \(\frac{1}{2}-\frac{1}{504}=\frac{251}{504}\)

Không Tên làm rõ được không

A =$\genfrac{}{}{0ex}{}{1}{2.9}+\genfrac{}{}{0ex}{}{1}{9.7}+\genfrac{}{}{0ex}{}{1}{7.19}+...+\genfrac{}{}{0ex}{}{1}{252.509}$

A = 2. ($\genfrac{}{}{0ex}{}{1}{4.9}+\genfrac{}{}{0ex}{}{1}{9.14}+\genfrac{}{}{0ex}{}{1}{14.19}+...+\genfrac{}{}{0ex}{}{1}{504.509}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$($\genfrac{}{}{0ex}{}{1}{4}-\genfrac{}{}{0ex}{}{1}{9}+\genfrac{}{}{0ex}{}{1}{9}-\genfrac{}{}{0ex}{}{1}{14}+\genfrac{}{}{0ex}{}{1}{14}-\genfrac{}{}{0ex}{}{1}{19}+...+\genfrac{}{}{0ex}{}{1}{504}-\genfrac{}{}{0ex}{}{1}{509}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$($\genfrac{}{}{0ex}{}{1}{4}-\genfrac{}{}{0ex}{}{1}{509}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$($\genfrac{}{}{0ex}{}{509}{2036}-\genfrac{}{}{0ex}{}{4}{2036}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$.$\genfrac{}{}{0ex}{}{505}{2036}$

A =$\genfrac{}{}{0ex}{}{101}{1018}$

A =$\genfrac{}{}{0ex}{}{1}{2.9}+\genfrac{}{}{0ex}{}{1}{9.7}+\genfrac{}{}{0ex}{}{1}{7.19}+...+\genfrac{}{}{0ex}{}{1}{252.509}$

A = 2. ($\genfrac{}{}{0ex}{}{1}{4.9}+\genfrac{}{}{0ex}{}{1}{9.14}+\genfrac{}{}{0ex}{}{1}{14.19}+...+\genfrac{}{}{0ex}{}{1}{504.509}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$($\genfrac{}{}{0ex}{}{1}{4}-\genfrac{}{}{0ex}{}{1}{9}+\genfrac{}{}{0ex}{}{1}{9}-\genfrac{}{}{0ex}{}{1}{14}+\genfrac{}{}{0ex}{}{1}{14}-\genfrac{}{}{0ex}{}{1}{19}+...+\genfrac{}{}{0ex}{}{1}{504}-\genfrac{}{}{0ex}{}{1}{509}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$($\genfrac{}{}{0ex}{}{1}{4}-\genfrac{}{}{0ex}{}{1}{509}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$($\genfrac{}{}{0ex}{}{509}{2036}-\genfrac{}{}{0ex}{}{4}{2036}$)

A =$\genfrac{}{}{0ex}{}{2}{5}$.$\genfrac{}{}{0ex}{}{505}{2036}$

A =$\genfrac{}{}{0ex}{}{101}{1018}$

A=7/81

Đặt \(A=\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{252.509}\)

\(\Leftrightarrow A=\frac{2}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)

\(\Leftrightarrow A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{504}-\frac{1}{509}\right)\)

\(\Leftrightarrow A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{509}\right)\)

\(\Leftrightarrow A=\frac{2}{5}.\frac{505}{2036}\)

\(\Leftrightarrow A=\frac{101}{1018}\)

~ Hok tốt ~

#)Giải :

\(A=\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{252.509}\)

\(A=\frac{2}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)

\(A=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{504}-\frac{1}{509}\right)\)

\(A=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{509}\right)\)

\(A=\frac{2}{5}\times\frac{505}{2036}\)

\(A=\frac{101}{1018}\)