Question

Tính :

\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)....\left(1-\frac{1}{210}\right)\)

Answer 1

\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{210}\right)\)

\(B=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{209}{210}\)

\(B=\frac{1}{3}.\frac{1}{3}.\frac{9}{2}.\frac{14}{15}...\frac{209}{210}\)

\(B=\frac{1}{6}.\frac{9}{2}.\frac{14}{15}...\frac{209}{210}\)

\(B=\frac{1}{2}.\frac{1}{1}.\frac{7}{5}...\frac{209}{210}\)

\(B=\frac{7}{10}...\frac{209}{210}\)

\(B=\frac{62}{210}\)