Tính tích sau, rồi tìm số nghịch đảo của kết quả
- T = (1-\(\frac{1}{3}\)) (1-\(\frac{1}{5}\)) (1-\(\frac{1}{7}\)) (1-\(\frac{1}{9}\)) (1-\(\frac{1}{11}\)) (1-\(\frac{1}{2}\)) (1-\(\frac{1}{4}\)) (1-\(\frac{1}{6}\)) (1-\(\frac{1}{8}\)) (1-\(\frac{1}{10}\))
\(T=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{5}\right)\left(1-\frac{1}{7}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{11}\right)\left(1-\frac{1}{2}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{8}\right)\left(1-\frac{1}{10}\right)\)
\(T=\frac{2}{3}.\frac{4}{5}.\frac{6}{7}.\frac{8}{9}.\frac{10}{11}.\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}.\frac{9}{10}=\frac{\left(2.4.6.8.10\right).\left(1.3.5.7.9\right)}{\left(3.5.7.9.11\right).\left(2.4.6.8.10\right)}=\frac{1}{11}\)
Đáp số: T=1/11