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\(\left(1-\frac{1}{97}\right)x\left(1-\frac{1}{98}\right)x...x\left(1-\frac{1}{1000}\right)\)
\(\frac{96}{97}\cdot x\cdot\frac{97}{98}\cdot x\cdot...\cdot x\cdot\frac{999}{1000}\)
\(\frac{96}{97}\cdot\frac{97}{98}\cdot...\cdot\frac{999}{1000}\cdot x^{903}\)
\(\frac{96}{1000}\cdot x^{903}\)
\(\frac{12}{125}\cdot x^{903}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(1-1/97),(1-1/98).....(1-1/1000)
=96/97.97/98.....999/1000
=(96.97...999)/(97.98...1000)
=96/1000=12/125
Dấu . Là dấu nhân nhé
=\(\frac{96}{97}\)x\(\frac{97}{98}\)x...x\(\frac{999}{1000}\)
triệt tiêu đi ta có:
=\(\frac{96}{1000}\)=\(\frac{12}{125}\)
tick nhé!!
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(\left(1-\frac{1}{97}\right)\times\left(1-\frac{1}{98}\right)\times.....\times\left(1-\frac{1}{1000}\right).\)
\(=\frac{97-1}{97}\times\frac{98-1}{98}\times.....\times\frac{1000-1}{1000}\)
\(=\frac{96}{97}\times\frac{97}{98}\times....\times\frac{999}{1000}\) (rút gọn hết )
\(=\frac{96}{1000}\)
\(=\frac{12}{125}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(1 - 1/97) x (1 - 1/98) x ... x (1 - 1/1000)
= 96/97 x 97/98 x ... x 999/1000
= 12/125
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(1-\frac{1}{97}\right)x\left(1-\frac{1}{98}\right)x....x\left(1-\frac{1}{1000}\right)\)
\(A=\frac{96}{97}x\frac{97}{98}x..x\frac{999}{1000}\)
\(A=\frac{96x97x98x...x999}{97x98x99x...x1000}=\frac{96}{1000}=\frac{12}{125}\)
=\(\frac{96}{1000}\)