Question

P=(1-1/2).(1-1/3).(1-1/4).(1-1/5)....(1-1/2011).(1-1/2012)

Answer 1

\(P=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right).\left(1-\dfrac{1}{5}\right)...\left(1-\dfrac{1}{2011}\right).\left(1-\dfrac{1}{2012}\right)\)

\(\Leftrightarrow P=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}...\dfrac{2010}{2011}.\dfrac{2011}{2012}\)

\(\Leftrightarrow P=\dfrac{1.2.3.4...2010.2011}{2.3.4.5...2011.2012}\)

\(\Leftrightarrow P=\dfrac{1}{2012}\)

Vậy \(P=\dfrac{1}{2012}\).