Question

\(\left(1-\dfrac{1}{7}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{3}{7}\right)...\left(1-\dfrac{2014}{7}\right)\)

Answer 1

\(=\dfrac{6}{7}\cdot\dfrac{5}{7}\cdot\dfrac{4}{7}\cdot\dfrac{3}{7}\cdot\dfrac{2}{7}\cdot\dfrac{1}{7}\cdot\dfrac{0}{7}\cdot...\cdot\dfrac{-2007}{7}\)

=0