Question

A=(1-1/2).(1-1/3).(1-1/4)...(1-1/20)

Answer 1

\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{20}\right)\) 

\(A=\frac{1}{2}.\frac{2}{3}....\frac{19}{20}\) 

\(A=\frac{1.2.3....19}{2.3.4...20}=\frac{1}{20}\)

Answer 2

A = (1 -1/2).( 1 -1/3).(1-1/4)...(1-1/20)

A = 1/2.2/3.3/4...19/20

A = 1.2.3....19/2.3.4...20

A = 1/20