Question

(1-1/2) *(1-1/3) *(1-1/4) *(1-1/5) * (1-1/6) * (1-1/7) =

Answer 1

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\)

\(=\frac{1\times2\times3\times4\times5\times6}{2\times3\times4\times5\times6\times7}\)

\(=\frac{1}{7}\)

Answer 2

Quá dễ:

\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot...\cdot\left(1-\frac{1}{7}\right)\)=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\)=\(\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6}{2\cdot3\cdot4\cdot5\cdot6\cdot7}\)=\(\frac{1}{7}\)