Question

( 1- 1/2 ) x ( 1 - 1/3 ) x ( 1 - 1/4 ) x .......x ( 1 - 1/9 )

Answer 1

\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times\cdot\cdot\cdot\times\left(1-\dfrac{1}{9}\right)\)

\(=\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times\cdot\cdot\cdot\times\dfrac{8}{9}\)

\(=\dfrac{1\times2\times3\times\cdot\cdot\cdot\times8}{2\times3\times4\times\cdot\cdot\cdot\times8\times9}\)

\(=\dfrac{1}{9}\)

Answer 2

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{8}{9}\)

=1/9