Question

(1-1/2).(1-1/3).(1-1/4)...(1-1/1999).(1-1/2000)

Answer 1

\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{1999}\right)\left(1-\frac{1}{2000}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{1998}{1999}.\frac{1999}{2000}=\frac{1.2.3...1998.1999}{2.3.4...1999.2000}=\frac{1}{2000}\)

Answer 2

\(\left(1-\frac{1}{2}\right).\left(1.\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{1999}\right).\left(1-\frac{1}{2000}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{1998}{1999}.\frac{1999}{2000}\)

\(=1.\frac{1}{2000}\)

\(=\frac{1}{2000}\)