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\(\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times..........\times\left(1+\frac{1}{2005}\right)\)
=\(\frac{3}{2}\times\frac{4}{3}\times............\times\frac{2006}{2005}\)
=\(\frac{2006}{2}=1003\)
a)\(=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times...\times\left(\dfrac{2005}{2005}+\dfrac{1}{2005}\right)\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times...\times\dfrac{2006}{2005}=\dfrac{2006}{2}=1003\)
b)\(=\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\times\dfrac{1}{2}=\dfrac{3}{3}\times\dfrac{1}{2}=\dfrac{1}{2}\)
\(\left(1-\frac{1}{99}\right)\left(1-\frac{1}{100}\right).....\left(1-\frac{1}{2005}\right)\)
\(=\frac{98}{99}.\frac{99}{100}.....\frac{2004}{2005}=\frac{98}{2005}\)
2005 x 2007 - \(\frac{1}{2004}\)+ 2005 x 2006
= 4024035 - \(\frac{1}{2004}\)+ 4022030
= 4024035 + 4022030
= 8046065
\(\frac{2005.2007-1}{2004+2005.2006}=\frac{2005.2006+2005-1}{2004+2005.2006}=\frac{2005.2006+2004}{2004+2005.2006}=1\)
K CHO MIK NHA!