Question

( 1-1/2) . (1-1/3) . (1-1/4). (1-1/5 )...(1-1/2003 ) . (1-1/2004) .

Answer 1

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{2002}{2003}.\frac{2003}{2004}\)

\(=\frac{1.2.3.4...2002.2003}{2.3.4.5...2003.2004}\)

\(=\frac{1}{2004}\)

Answer 2

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right)...\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{2002}{2003}.\frac{2003}{2004}\)

\(=\frac{1}{2004}\)