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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 )
\(=\frac{96}{1000}\)
\(=\frac{12}{125}\)
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right).100-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right).100-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\left(1-\frac{1}{10}\right).100-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(90-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=1\)
\(\frac{5}{2}:\left(x+\frac{266}{100}\right)=\frac{1}{2}\Rightarrow x+\frac{266}{100}=5\Rightarrow x=\frac{117}{50}\)
Vậy x = 117/50
Ta có:
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right).100\\ =\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right).100\)
\(=\left(1-\frac{1}{10}\right).100\)
\(=\frac{9}{10}.100\)
= 90
Khi đó đề bài sẽ thành : \(90-\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=89\)
\(\Rightarrow\left[\frac{5}{2}:\left(x+\frac{266}{100}\right)\right]:\frac{1}{2}=1\)
\(\Rightarrow\frac{5}{2}:\left(x+\frac{266}{100}\right)=\frac{1}{2}\)
\(\Rightarrow x+\frac{266}{100}=5\)
\(\Rightarrow x=\frac{117}{50}\)
Vậy \(x=\frac{117}{50}\)
\(\left(1-\frac{1}{97}\right)x\left(1-\frac{1}{98}\right)x...x\left(1-\frac{1}{1000}\right)\)
\(\frac{96}{97}\cdot x\cdot\frac{97}{98}\cdot x\cdot...\cdot x\cdot\frac{999}{1000}\)
\(\frac{96}{97}\cdot\frac{97}{98}\cdot...\cdot\frac{999}{1000}\cdot x^{903}\)
\(\frac{96}{1000}\cdot x^{903}\)
\(\frac{12}{125}\cdot x^{903}\)
a/
\(1\frac{1}{2}x1\frac{1}{3}x1\frac{1}{4}x1\frac{1}{5}x1\frac{1}{6}=\frac{3}{2}x\frac{4}{3}x\frac{5}{4}x\frac{6}{5}x\frac{7}{6}=\frac{7}{2}=3\frac{1}{2}\)
b/
x=0; y=5
(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!!