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T = \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{624}{625}\)
T = \(\frac{1.3.2.4.3.5.....24.26}{2.2.3.3.4.4.....25.25}\)
T = \(\frac{\left(1.2.3.....24\right)\left(3.4.5.....26\right)}{\left(2.3.4.....25\right)\left(2.3.4.....25\right)}\)
T = \(\frac{26}{25.2}\)
T = \(\frac{13}{25}\)
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a,Đặt \(A=\frac{1}{1\times4}+\frac{1}{4\times7}+...+\frac{1}{97\times100}\)
\(\Rightarrow3A=\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{97\times100}\)
\(\Rightarrow3A=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)
\(\Rightarrow3A=1-\frac{1}{100}=\frac{99}{100}\)
\(\Rightarrow A=\frac{99}{300}\)
b, \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{99}{100}=\frac{1\times2\times...\times99}{2\times3\times...\times1000}=\frac{1}{100}\)
c, \(\frac{3}{4}\times\frac{8}{9}\times...\times\frac{99}{100}=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times...\times\frac{9.11}{10.10}=\frac{1.2.....9}{2.3.....10}\times\frac{3.4.....11}{2.3.....10}=\frac{1}{10}\times\frac{11}{2}=\frac{11}{20}\) (dấu . là dấu nhân)
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a; 2,5 \(\times\) \(x\) + 3,7 \(\times\) \(x\) - 4,8 \(\times\) \(x\) + 216,5 \(\times\) 8 = 2012
\(x\) \(\times\) (2,5 + 3,7 - 4,8) + 1732 = 2012
\(x\) \(\times\) 1,4 + 1732 = 2012
\(x\) \(\times\) 1,4 = 2012 - 1732
\(x\) \(\times\) 1,4 = 280
\(x\) = 280 : 1,4
\(x\) = 200
b; \(\dfrac{3}{4}\) - \(\dfrac{1}{4}\) : \(x\) = \(\dfrac{1}{6}\)
\(\dfrac{1}{4}\) : \(x\) = \(\dfrac{3}{4}\) - \(\dfrac{1}{6}\)
\(\dfrac{1}{4}\) : \(x\) = \(\dfrac{7}{12}\)
\(x\) = \(\dfrac{1}{4}\) : \(\dfrac{7}{12}\)
\(x\) = \(\dfrac{3}{7}\)
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\(2\frac{3}{13}\cdot\frac{26}{58}\cdot4\cdot2\frac{15}{24}\cdot\frac{8}{21}=\frac{29}{13}\cdot\frac{26}{58}\cdot4\cdot\frac{21}{8}\cdot\frac{8}{21}=\frac{29\cdot26\cdot4\cdot21\cdot8}{13\cdot58\cdot8\cdot21}=\frac{1\cdot2\cdot4\cdot1\cdot1}{1\cdot2\cdot1\cdot1}=\frac{1\cdot4}{1}=4\)