Tìm x, biết:
x = ( \(6\frac{3}{5}\) : 6 - 0,125 . 8 + \(\frac{2}{15}\) . 0,03 ) . \(\frac{11}{4}\)
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\(\Rightarrow x=\left(\frac{33}{5}.\frac{1}{6}-\frac{1}{8}.8+\frac{2}{15}.\frac{3}{100}\right).\frac{11}{4}\)
\(=\left(\frac{11}{10}-1+\frac{1}{250}\right).\frac{11}{4}=\frac{13}{125}.\frac{11}{4}=\frac{143}{500}\)
\(\Rightarrow x=\left(\frac{33}{5}.\frac{1}{6}-\frac{1}{8}.8+\frac{2}{15}.\frac{3}{100}\right).\frac{11}{4}\)
\(\Rightarrow x=\left(\frac{11}{10}-1+\frac{1}{250}\right).\frac{11}{4}=\frac{13}{125}.\frac{11}{4}=\frac{143}{500}\)
\(a,A=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+...+\frac{3}{90}\)
\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=3.\left(1-\frac{1}{10}\right)\)
\(A=3.\frac{9}{10}=\frac{27}{10}\)
\(b,B=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(B.\frac{3}{2}=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{17}\)
\(B=\frac{15}{34}:\frac{3}{2}=\frac{5}{17}\)
\(\frac{-15}{4}\times\frac{9}{11}+\frac{15}{4}\times\frac{15}{11}-\frac{15}{4}\times\frac{6}{11}\)
\(=\frac{15}{4}\times\left(\frac{-9}{11}+\frac{15}{11}-\frac{6}{11}\right)\)
\(=\frac{15}{4}\times0\)
\(=0\)
\(=\frac{15}{4}\times\left(-\frac{9}{11}\right)+\frac{15}{4}\times\frac{15}{11}+\frac{15}{4}\times\left(-\frac{6}{11}\right)\)
\(=\frac{15}{4}\times\left(-\frac{9}{11}+\frac{15}{11}+\left(-\frac{6}{11}\right)\right)\)
\(=\frac{15}{4}\times0\)
\(=0\)
Đặt \(B=\frac{1}{1.2}+\frac{5}{2.7}+\frac{8}{7.15}+\frac{13}{15.28}+\frac{21}{28.49}+\frac{32}{49.81}\)
\(\Rightarrow B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}+\frac{1}{28}-\frac{1}{49}+\frac{1}{49}-\frac{1}{81}\)
\(\Rightarrow B=1-\frac{1}{81}\)
\(\Rightarrow B=\frac{80}{81}\)
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