Bạn alibaba nguyễn giải đúng rồi nhưng mình nghĩ cách này sẽ nhanh hơn :
Giải :
Đặt : \(A=\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)........\left(1-\frac{1}{1326}\right)\)
\(\Rightarrow A=\left(1-\frac{2}{6.7}\right)\left(1-\frac{2}{7.8}\right)\left(1-\frac{2}{8.9}\right).......\left(1-\frac{2}{51.52}\right)\)
\(\Rightarrow A=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}.........\frac{50.53}{51.52}\)
\(\Rightarrow A=\frac{\left(5.6.7......50\right)\left(8.9.10......53\right)}{\left(6.7.8.....51\right)\left(7.8.9......52\right)}\)
\(\Rightarrow A=\frac{5}{51}.\frac{53}{7}\)
\(\Rightarrow A=\frac{265}{357}\)
Vậy : \(\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)......\left(1-\frac{1}{1326}\right)=\frac{265}{357}\)
\(\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)...\left(1-\frac{1}{1326}\right)\)
\(=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}...\frac{1325}{1326}\)
\(=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}...\frac{2650}{2652}\)
\(=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}...\frac{50.53}{51.52}\)
\(=\frac{5}{7}.\frac{53}{51}=\frac{265}{357}\)
\(\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)...\left(1-\frac{1}{1326}\right)\)
\(=\frac{20}{21}.\frac{27}{28}......\frac{1325}{1326}\)
\(=\frac{40}{42}.\frac{54}{56}......\frac{2650}{2652}\)
\(=\frac{5.8}{6.7}.\frac{6.9}{7.8}.......\frac{50.53}{51.52}\)
\(=\frac{5}{7}.\frac{8}{6}.\frac{6}{8}.....\frac{50}{52}.\frac{53}{51}\)
\(=\frac{5.8.6.....50.53}{7.6.8.....52.51}\)
\(=\frac{5.53}{7.51}\)
\(=\frac{265}{375}\)
cai bai nay co tren tok day ban len tok xem di ban hien
