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(1-1/97) x (1-1/98) x (1-1/99) x (1-1/1000) = 96/97 x 97/98 x 98/99 x 999/1000
= 96 x 97 x 98 x 999 / 97 x 98 x 99 x 1000 = 12 x 111 / 11 x 125 = 1332 / 1375
\(C=\left(1-\frac{1}{97}\right).\left(1-\frac{1}{98}\right).\left(1-\frac{1}{99}\right)......\left(1-\frac{1}{1000}\right)\)
\(C=\frac{96}{97}.\frac{97}{98}.\frac{98}{99}........\frac{999}{1000}\)
\(C=\frac{96}{1000}\)
\(C=\frac{12}{125}\)
B=3/2x4/3x...........x2018/2017
=3x4x5x...........x2018/2x3x2x2x............x2017
=2x2018
=4036
A,C tương tự
( 1- 1/97) x ( 1- 1/98) x … x ( 1-1/1000)
= 96/97 x 97/98 x ….x 999/1000
= 96/1000
= 12/125
(1-1/97)x(1-1/98)x....x(1-1/1000)
=96/97 x 97/98 x ... x 999/1000
= 96/1000
= 12/125
\(=\frac{96}{97}\cdot\frac{97}{98}\cdot...\cdot\frac{999}{1000}=\frac{96\cdot97\cdot...\cdot999}{97\cdot98\cdot...\cdot999\cdot1000}=\frac{96}{1000}=\frac{12}{125}\)
Bài làm
\(\left(1-\frac{1}{97}\right)x\left(1-\frac{1}{98}\right)x...x\left(1-\frac{1}{1000}\right)\)
= \(\left(\frac{97}{97}-\frac{1}{97}\right)x\left(\frac{98}{98}-\frac{1}{98}\right)x...x\left(\frac{1000}{1000}-\frac{1}{1000}\right)\)
= \(\frac{96}{97}x\frac{97}{98}x...x\frac{999}{1000}\)
= \(\frac{96}{1000}\)
= \(\frac{12}{125}\)
# Chúc bạn học tốt #
(1 - 1/97) .(1 - 1/98)....(1 - 1/1000)
= (97/97 - 1/97).(98/98 - 1/98) ... (1000/1000 - 1/1000)
= 96/97 . 97/98....999/1000
= 96.97....999/97.98.....1000
= 96/1000
= 12/125
\(1-\frac{1}{97}.1-\frac{1}{98}.1-\frac{1}{99}.....1-\frac{1}{1000}\)
\(=\frac{96}{97}.\frac{97}{98}.\frac{98}{99}.....\frac{999}{1000}\)
\(=\frac{96}{1000}\)
\(=\frac{12}{125}\)