Question

( 1-1/4)x(1- 1/9) x ( 1-1\16)x(1-1\25)x(1-1\36) =

Answer 1

\(\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{36}\right)\)

\(=\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times...\times\left(1-\dfrac{1}{6}\right)\times\left(1+\dfrac{1}{2}\right)\times\left(1+\dfrac{1}{3}\right)\times...\times\left(1+\dfrac{1}{6}\right)\)

\(=\dfrac{1}{2}\times\dfrac{2}{3}\times...\times\dfrac{5}{6}\times\dfrac{3}{2}\times\dfrac{4}{3}\times...\times\dfrac{7}{6}\)

\(=\dfrac{1}{6}\times\dfrac{7}{2}=\dfrac{7}{12}\)