\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times...\times\left(1-\frac{1}{2003}\right)\times\left(1-\frac{1}{2004}\right)\)
\(=\left(\frac{2}{2}-\frac{1}{2}\right)\times\left(\frac{3}{3}-\frac{1}{3}\right)\times...\times\left(\frac{2003}{2003}-\frac{1}{2003}\right)\times\left(\frac{2004}{2004}-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)
\(=\frac{1\times2\times...\times2002\times2003}{2\times3\times...\times2003\times2004}=\frac{1}{2004}\)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2004}\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{2003}{2004}=\frac{1\cdot2\cdot3\cdot...\cdot2003}{2\cdot3\cdot4\cdot...\cdot2004}=\frac{1}{2004}\)
bài này chúng mày còn ngu tiêu đây làm 1 bước cũng được 5 điểm 1 bài toán
