(1-\(\dfrac{1}{2}\))\(\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{14}\right).................\left(1-\dfrac{1}{2011}\right)\)
=\(\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.......\dfrac{2010}{2011}\)
=\(\dfrac{1.2.3.4.....2010}{2.3.4.....2011}\)
=\(\dfrac{1}{2011}\)