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\(C=70.\left(131313.\left(\dfrac{1}{565656}+\dfrac{1}{727272}+\dfrac{1}{909090}\right)\right)\)
\(C=70.\left(131313.\dfrac{1}{235690}\right)\)
\(C=70.\dfrac{39}{70}\)
\(C=39\)
y =2(\(\frac{37\cdot10101}{120\cdot10101}\)-\(\frac{37\cdot10101}{6\cdot10101}\)):\(\frac{1}{x}\)=-37
y=2(37/120-37/6):1/x=-37
y=2(37/120-740/120):1/x=-37
y=2.(-703/120):1/x=-37
y=--703/60:1/x=-37
1/x=-703/60:-37
1/x=19/60
x=60/19
a: \(=\dfrac{13\left(3-18\right)}{40\left(15-2\right)}=\dfrac{13}{15-2}\cdot\dfrac{-15}{40}=\dfrac{-3}{8}\)
b: \(=\dfrac{18\left(34-124\right)}{36\left(-17-13\right)}=\dfrac{1}{2}\cdot\dfrac{-90}{-30}=\dfrac{3}{2}\)
c: \(=\dfrac{3\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}{4\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}+\dfrac{\dfrac{-1}{4}\cdot\dfrac{-2}{3}-\dfrac{3}{4}:\dfrac{1}{6}}{\dfrac{3}{2}\cdot\left(\dfrac{-2}{3}-\dfrac{3}{4}\cdot\dfrac{-2}{3}\right)}\)
\(=\dfrac{3}{4}+\dfrac{\dfrac{2}{12}-\dfrac{9}{2}}{\dfrac{3}{2}\cdot\dfrac{-1}{6}}=\dfrac{3}{4}+\dfrac{-13}{3}:\dfrac{-3}{12}=\dfrac{3}{4}+\dfrac{13}{3}\cdot\dfrac{12}{3}\)
\(=\dfrac{3}{4}+\dfrac{156}{9}=\dfrac{217}{12}\)
\(-3+\dfrac{2}{5}=\dfrac{-13}{5}\)
\(\dfrac{-312}{936}+\dfrac{-373737}{151515}=\dfrac{-14}{5}\)
\(\dfrac{-3}{8}-\dfrac{5}{12}=\dfrac{-19}{24}\)
1: \(S=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{101}{100}=\dfrac{101}{2}\)
2: \(B=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2006}{2007}=\dfrac{1}{2007}\)
a)
\(A=\dfrac{3}{4}.\dfrac{8}{9}...\dfrac{9999}{10000}\)
\(=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}...\dfrac{99.101}{100.100}\)
\(=\dfrac{1.2...99}{2.3...100}.\dfrac{3.4...101}{2.3...100}\)
\(=\dfrac{1}{100}.\dfrac{101}{2}\)
\(=\dfrac{101}{200}\)
1. \(A=\dfrac{2\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{11}\right)}{4\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{11}\right)}=\dfrac{2}{4}=\dfrac{1}{2}\)
2. \(B=\dfrac{1^2.2^2.3^2.4^2}{1.2^2.3^2.4^2.5}=\dfrac{1}{5}\)
3.\(C=\dfrac{2^2.3^2.\text{4^2.5^2}.5^2}{1.2^2.3^2.4^2.5.6^2}=\dfrac{125}{36}\)
4.D=\(D=\left(\dfrac{4}{5}-\dfrac{1}{6}\right).\dfrac{4}{9}.\dfrac{1}{16}=\dfrac{19}{30}.\dfrac{1}{36}=\dfrac{19}{1080}\)
\(27\cdot\left(\dfrac{373737}{424242}+\dfrac{373737}{565656}+\dfrac{373737}{727272}\right)\\ =27\cdot\left(\dfrac{37}{42}+\dfrac{37}{56}+\dfrac{37}{72}\right)\\ =27\cdot37\cdot\left(\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)\\ =999\cdot\left(\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}\right)\\ =999\cdot\left(\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\\ =999\cdot\left(\dfrac{1}{6}-\dfrac{1}{9}\right)\\ =999\cdot\dfrac{1}{18}\\ =\dfrac{111}{2}\)
\(27.\left(\dfrac{373737}{424242}+\dfrac{373737}{565656}+\dfrac{373737}{727272}\right)=\dfrac{111}{2}\)