Question

[Đỗ lệ dung]

A=1/3+13/15+33/35+61/63+97/99+141/143

Answer 1

[Capheny Bản Quyền]

\(A=1-\frac{2}{3}+1-\frac{2}{15}+1-\frac{2}{35}+1-\frac{2}{63}+1-\frac{2}{99}+1-\frac{2}{143}\)      

\(=1+1+1+1+1+1-\frac{2}{3}-\frac{2}{15}-\frac{2}{35}-\frac{2}{63}-\frac{2}{99}-\frac{2}{143}\)   

\(=6-\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+\frac{2}{143}\right)\)   

\(=6-\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)\)   

\(=6-\left(1-\frac{1}{13}\right)\)   

\(=6-1+\frac{1}{13}\)   

\(=5+\frac{1}{13}\)   

\(=\frac{65}{13}+\frac{1}{13}\)   

\(=\frac{66}{13}\)