Bài 1
\(\left(1-\dfrac{1}{99}\right)\times\left(1-\dfrac{1}{100}\right)\times...\times\left(1-\dfrac{1}{2006}\right)\)
\(=\dfrac{98}{99}\times\dfrac{99}{100}\times...\times\dfrac{2005}{2006}\)
\(=\dfrac{98}{2006}\)
\(=\dfrac{49}{1003}\)
Bài 2
\(\dfrac{111}{333}=\dfrac{111:111}{333:111}=\dfrac{1}{3}\)
\(\dfrac{2222}{4444}=\dfrac{2222:2222}{4444:2222}=\dfrac{1}{2}\)
Do \(3>2\Rightarrow\dfrac{1}{3}< \dfrac{1}{2}\)
Vậy \(\dfrac{111}{333}< \dfrac{2222}{4444}\)
Bài 1.
\(\left(1-\dfrac{1}{99}\right)\times\left(1-\dfrac{1}{100}\right)\times...\times\left(1-\dfrac{1}{2006}\right)\)
\(=\dfrac{98}{99}\times\dfrac{99}{100}\times...\times\dfrac{2005}{2006}\)
\(=\dfrac{98\times99\times...\times2005}{99\times100\times...2006}\)
\(=\dfrac{98}{2006}\)
\(=\dfrac{49}{1003}\)
Bài 2.
Có: \(\dfrac{111}{333}=\dfrac{111}{3\times111}=\dfrac{1}{3}\)
\(\dfrac{2222}{4444}=\dfrac{2222}{2\times2222}=\dfrac{1}{2}\)
Vì \(\dfrac{1}{3}< \dfrac{1}{2}\) nên \(\dfrac{111}{333}< \dfrac{2222}{4444}\)
