Ta có: \(\left(1-\frac{1}{1007}\right)\times\left(1-\frac{1}{1008}\right)\times...\times\left(1-\frac{1}{1011}\right)\times\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\times\frac{1007}{1008}\times...\times\frac{1010}{1011}\times\frac{1011}{1012}\)
\(=\frac{1006}{1012}=\frac{503}{506}\)
\(\left(1-\frac{1}{1007}\right)\cdot\left(1-\frac{1}{1008}\cdot\right)...\cdot\left(1-\frac{1}{1011}\right)\cdot\left(1-\frac{1}{1012}\right)\)
\(=\frac{1006}{1007}\cdot\frac{1007}{1008}\cdot...\cdot\frac{1010}{1011}\cdot\frac{1011}{1012}\)
\(=\frac{1006.1007\cdot..\cdot2010\cdot2011}{1007\cdot1008\cdot....\cdot1011.1012}\)
\(=\frac{1006}{1012}\)
\(=\frac{503}{506}\)
Cảm ơn m.n nha, ko ngờ lại có kết quả nhanh như vậy(=^-ω-^=)
