(1-1/99).(1-1/100)....(1-1/2006) =(99/99-1/99).(100/100-1/100)....(2006/2006-1/2006) = (98/99).(99/100)...(2005/2006) =98/2006=..

\(\left(1-\frac{1}{99}\right)\times\left(1-\frac{1}{100}\right)\times...\times\left(1-\frac{1}{2006}\right)\)

\(=\left(\frac{99}{99}-\frac{1}{99}\right)\times\left(\frac{100}{100}-\frac{1}{100}\right)\times\left(\frac{2006}{2006}-\frac{1}{2006}\right)\)

\(=\frac{98}{99}\times\frac{99}{100}\times...\times\frac{2005}{2006}\)

\(=\frac{98\times99\times...\times2005}{99\times100\times...\times2006}\)

\(=\frac{98}{2006}=\frac{49}{1003}\)

= 49\1003 đung ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

Ta có : \(\left(1\frac{1}{99}\right)\times\left(1\frac{1}{100}\right)\times...\times\left(1\frac{1}{2006}\right)\)

\(=\) \(\frac{100}{99}\times\frac{101}{100}\times...\times\frac{2007}{2006}\)      

\(=\)  \(\frac{100\times101\times...\times2007}{99\times100\times...\times2006}\)

\(=\)    \(\frac{2007}{99}\)

\(=\)    \(\frac{223}{11}\)

        Đánh máy mệt v~~ Haizzz ...

P/s :  Bn cứ lm` theo mk là OK ko cần bàn cãi =))

                                 > Chúc họk tốt <

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 \(\dfrac{111}{333}< \dfrac{2222}{4444}\)

trong tích đã cho từ 1-1/99 đến 1-2006 sẽ có 1 thừa số bằng 1-1=0

=>tích đã cho bằng 0

Tinh bang cach thuan tien nha mn

Ta có : \(\left(1-\frac{1}{99}\right)\text{ x }\left(1-\frac{1}{100}\right)\text{ x }.....\text{ x }\left(1-\frac{1}{2006}\right)\)

\(=\frac{98}{99}\text{ x }\frac{99}{100}\text{ x }\frac{100}{101}\text{ x }......\text{ x }\frac{2005}{2006}\)

\(=\frac{98\text{ x }99\text{ x }100\text{ x }......\text{ x }2005}{99\text{ x }100\text{ x }101\text{ x }......\text{ x }2006}\)

\(=\frac{98}{2006}=\frac{49}{1003}\)

$1-\frac{1}{99}x1-\frac{1}{100}....1-\frac{1}{2006}$
=($\frac{99}{99}-\frac{1}{99}$)x($\frac{100}{100}-\frac{1}{100}$)....($\frac{2006}{2006}-\frac{1}{2006}$) = $\frac{98}{99}x\frac{99}{100}....\frac{2005}{2006}=\frac{98}{2006}$

$\frac{\mathrm{NÈ\; EM}}{}$