Question

(1-1/2) . (1-1/3) . (1-1/4).....(1-1/2013) = ?

Answer 1

=1/2 x 2/3 x 3/4 x … x 2012/2013 

=1 x 2 x 3 x … x 2012 /  2 x 3 x 4 x … x 2013

=1/2013

Answer 2

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\cdot...\cdot\left(1-\frac{1}{2013}\right)\)\(=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{2012}{2013}=\frac{1\cdot2\cdot3\cdot...\cdot2012}{2\cdot3\cdot...\cdot2012\cdot2013}=\frac{1}{2013}\)