1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1 x 2000 = ?
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\dfrac{2+1}{2}\right)\left(\dfrac{3+1}{3}\right)\left(\dfrac{4+1}{4}\right)...\left(\dfrac{2000+1}{2000}\right)\)
\(=\dfrac{3.4.5...2001}{2.3.4...2000}=\dfrac{2001}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:A=(1−12)×(1−13)×.......×(1−12000)A=(1−12)×(1−13)×.......×(1−12000)
=12×23×34×..........×19992000=12×23×34×..........×19992000
=12000=12000
Vậy giá trị của A là:12000
\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{2001}{2000}=\dfrac{2001}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\left(1+\frac{1}{2005}\right)\left(1+\frac{1}{2006}\right)...\left(1+\frac{1}{2020}\right)\)
\(=\frac{2006}{2005}\cdot\frac{2007}{2006}\cdot...\cdot\frac{2021}{2020}\)
\(=\frac{2021}{2005}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:\(A=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times.......\times\left(1-\frac{1}{2000}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times..........\times\frac{1999}{2000}\)
\(=\frac{1}{2000}\)
Vậy giá trị của A là:\(\frac{1}{2000}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\dfrac{20}{21}x\dfrac{21}{22}x\dfrac{22}{23}x...x\dfrac{1999}{2000}\)
\(=\dfrac{20}{2000}=\dfrac{1}{100}\)
=20/21x21/22x22/23x..............x1998/1999x1999/2000
=20x21x22x23x.....................x1998x1999/21x22x23x24x...............x1999x2000
=20/2000
1/100
![](https://rs.olm.vn/images/avt/0.png?1311)
A = ( 1 - 1/2 ) . ( 1 - 1/3 ) . ( 1 - 1/4 ) . ... . ( 1 - 1/2000)
A = ( 2/2 - 1/2 ) . ( 3/3 - 1/3 ) . ( 4/4 - 1/4 ) . ... . ( 2000/2000 - 1/2000 )
A = 1/2 . 2/3 . 3/4 . ... . 1999/2000
A = 1.(2.3. ... . 1999)/ (2.3.4. ... .1999).2000
A = 1/2000
B = ( 1 + 1/2 ).(1 + 1/3 ).( 1+ 1/4 ). ... .(1+1/2000)
B = ( 2/2 + 1/2 ).(3/3+1/3).(4/4+1/4). ... .(1+1/2000)
B = 3/2.4/3.5/4. ... .2001/2000
B = (3.4.5. ... .2000).2001/2.(3.4. ... .2000)
B = 2001/2
B = 1000,5
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