B = \(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x........x\left(1-\frac{1}{2003}\right)x\left(1-\frac{1}{2004}\right)\)
B = \(\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x.........x\frac{2002}{2003}x\frac{2003}{2004}\)
=> B = \(\frac{1}{2004}\)
\(B=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2003}\right)\times\left(1-\frac{1}{2004}\right)\)
\(B=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)
\(B=\frac{1\times2\times3\times...\times2002\times2003}{2\times3\times4\times...\times2003\times2004}\)
\(\Rightarrow B=\frac{1}{2004}\)
Ta có:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right)....\left(1-\frac{1}{2003}\right).\left(1-\frac{1}{2004}\right)\)
\(B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2002}{2003}.\frac{2003}{2004}\)
\(B=\frac{1.2.3.4....2002.2003}{2.3.4.5....2003.2004}\)
\(\Rightarrow B=\frac{1}{2004}\)
