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\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times...\times\left(1-\frac{1}{2003}\right)\times\left(1-\frac{1}{2004}\right)\)
\(=\left(\frac{2}{2}-\frac{1}{2}\right)\times\left(\frac{3}{3}-\frac{1}{3}\right)\times...\times\left(\frac{2003}{2003}-\frac{1}{2003}\right)\times\left(\frac{2004}{2004}-\frac{1}{2004}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times...\times\frac{2002}{2003}\times\frac{2003}{2004}\)
\(=\frac{1\times2\times...\times2002\times2003}{2\times3\times...\times2003\times2004}=\frac{1}{2004}\)
\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2002}{2003}.\frac{2003}{2004}\)
Ta có : \(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}....\frac{2002}{2003}.\frac{2003}{2004}\)
\(=\frac{1.2.3.4.....2002.2003}{2.3.4.5....2003.2004}\)
\(=\frac{1}{2004}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{2003}{2004}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot2003}{2\cdot3\cdot4\cdot...\cdot2004}\)
\(=\frac{1}{2004}\)
a) 2005*2007-1 b)2003*2004+2005*10+1994
2004+2005*2006 2005*2004-2003*2004
c) ( 5+3/8+18+1/2-7-5/24 )
c) 5 + \(\frac{3}{8}\)+18 + \(\frac{1}{2}\) - 7 - \(\frac{5}{24}\)
=\(\frac{43}{8}\)+ \(\frac{35}{2}\) +\(\frac{163}{24}\)
=\(\frac{129}{24}\)+ \(\frac{420}{24}\)+\(\frac{163}{24}\)
= \(\frac{58}{51}\)
k nhé
={2003 x 2004 x 2005} x {2005 - 2005}
={2003 x 2004 x 2005} x 0
=0