Question

B=(1-1/2)(1-1/3)(1-1/4)...(1-1/2011)(1-1/2012)

Answer 1

\(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2010}{2011}\cdot\dfrac{2011}{2012}=\dfrac{1}{2012}\)

Answer 2

\(\Rightarrow B=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}....\dfrac{2011}{2012}\)

\(\Rightarrow B=\dfrac{1}{2012}\)