Question

tinh nhanh\(\left(1-\dfrac{1}{21}\right).\left(1-\dfrac{1}{28}\right)....\left(1-\dfrac{1}{1326}\right)\)

Answer 1

\(\left(1-\dfrac{1}{21}\right)\left(1-\dfrac{1}{28}\right)...\left(1-\dfrac{1}{1326}\right)\)

\(=\left(1-\dfrac{2}{42}\right)\left(1-\dfrac{2}{56}\right)\left(1-\dfrac{2}{72}\right)...\left(1-\dfrac{2}{2652}\right)\)

\(=\dfrac{40}{42}.\dfrac{54}{56}.\dfrac{70}{72}...\dfrac{2650}{2652}\)

\(=\dfrac{5.8}{6.7}.\dfrac{6.9}{7.8}.\dfrac{7.10}{8.9}...\dfrac{50.53}{51.52}\)

\(=\dfrac{5.6.7...50}{6.7.8...51}.\dfrac{8.9.10...53}{7.8.9...52}\)

\(=\dfrac{5}{51}.\dfrac{53}{7}=\dfrac{265}{357}\)