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a)
\(=\frac{3}{2}.\frac{4}{3}......\frac{100}{99}=\frac{100}{2}=50\)
b)
\(=\frac{\left(-1\right)}{2}.\frac{\left(-2\right)}{3}.....\frac{\left(-99\right)}{100}=\frac{-1}{100}\)
a,\(\frac{31}{1000}\)
b,\(\frac{8}{108}\)
c,0
a,\(\frac{49}{97}\)
b,\(\frac{-1}{4751}\)
\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.....\frac{899}{30^2}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{29.31}{30.30}=\frac{1.2.3.....29}{2.3.4.....30}.\frac{3.4.5.....31}{2.3.4.....30}\)
\(=\frac{1}{2}.\frac{31}{30}=\frac{31}{60}\)
1 A=\(\frac{31}{60}\)
2B=c,\(\frac{26\cdot32^{7}}{21}\approx4.25406\cdot10^{10}\)
3 C<\(\frac{1}{21}\)
4 D<\(\frac{11}{19}\)
a/
$(\frac{1}{2}+1)(\frac{1}{3}+1)....(\frac{1}{99}+1)$
$=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}$
$=\frac{3.4.5...100}{2.3.4...99}=\frac{100}{2}=50$
b/
$(\frac{1}{2}-1)(\frac{1}{3}-1)....(\frac{1}{100}-1)$
$=\frac{-1}{2}.\frac{-2}{3}.\frac{-3}{4}.....\frac{-99}{100}$
$=-\frac{1.2.3.4...99}{2.3.4...100}=-\frac{1}{100}$
Bài 1:
\(\Leftrightarrow-\dfrac{5}{7}:x=-\dfrac{7}{18}-\dfrac{1}{6}=\dfrac{-7}{18}-\dfrac{3}{18}=\dfrac{-10}{18}=\dfrac{-5}{9}\)
=>x=5/9:5/7=7/9
Bài 2:
a: \(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{1000}{999}=\dfrac{1000}{2}=500\)
b: \(=\dfrac{-1}{2}\cdot\dfrac{-2}{3}\cdot...\cdot\dfrac{-999}{1000}\)
\(=-\dfrac{1}{1000}\)
Câu c:
C = 3/2^2.8/3^2.15/4^2...99/10^2
C = \(\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\ldots\times\) \(\frac{9.11}{10.10}\)
C = \(\frac{1.2.3\ldots9}{2.3\ldots10}\) x \(\frac{3.4.\ldots11}{2.3.\ldots10}\)
C = \(\frac{1}{10}\) x \(\frac{11}{2}\)
C = 11/20
Bài 2:
a) \(\frac{4}{9}+x=\frac{-5}{3}\)
\(\Leftrightarrow x=\frac{-5}{3}-\frac{4}{9}\)
\(\Leftrightarrow x=\frac{-15}{9}-\frac{4}{9}\)\(=\frac{-19}{9}\)
Vậy: \(x=\frac{-19}{9}\)
b) \(2,4:\left(\frac{1}{2}.x-\frac{3}{4}\right)=\frac{3}{10}\)
\(\Leftrightarrow\frac{24}{10}:\left(\frac{1}{2}x-\frac{3}{4}\right)=\frac{3}{10}\)
\(\Leftrightarrow\frac{1}{2}x-\frac{3}{4}=\frac{24}{10}:\frac{3}{10}=\frac{24}{10}.\frac{10}{3}\)\(=8\)
\(\Leftrightarrow\frac{1}{2}x=8+\frac{3}{4}=\frac{35}{4}\)
\(\Leftrightarrow x=\frac{35}{4}:\frac{1}{2}=\frac{35}{4}.2=\frac{35}{2}\)
c) \(\frac{x+1}{-8}=\frac{-2}{x+1}\)
\(\Rightarrow\left(x+1\right).\left(x+1\right)=\left(-2\right).\left(-8\right)\)
\(\Leftrightarrow\left(x+1\right)^2=16=4^2=\left(-4\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x+1=4\\x+1=-4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)
Vậy: \(x\in\left\{3;-5\right\}\)
Bài 1:
1/6 + -5/7 : x = - 7/18
5/7: x = 1/6 + 7/18
5/7: x = 3/18 + 7/18
5/7: x = 5/9
x = 5/7 : 5/9
x = 5/7 x 9/5
x = 9/7
Vậy x = 9/7
Bài 2:
Câu a:
(1/2 + 1).(1/3 + 1).(1/4 + 1)...(1/999 + 1)
= (1/2 + 2/2).(1/3 + 3/3)...(1/999 + 999/999)
= 3/2.4/3....1000/999
= 1000/2
= 500
a.=2/3
b. 97/198