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\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}\right)\)
=\(\frac{1}{3}+\frac{1}{5}\)
=\(\frac{5}{3}\)
(3/10+4/5x1/2):1/8/9-1/1/3
=(3/10+4/10):17/9-4/3
=7/10:17/9-4/3
=63/170-4/3
=-491/510
\(=1-\frac{1}{3}+\frac{2}{3.5}+...+\frac{2}{15.17}\)
\(=1-\frac{1}{3}+2.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{15.17}\right)\)
\(=1-\frac{1}{3}+2.\left(\frac{1}{3}-\frac{1}{17}\right)\)
\(=\frac{62}{51}\)
\(\Leftrightarrow A=1-\frac{1}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{13.15}+\frac{2}{15.17}\)
\(\Leftrightarrow A=\frac{2}{1.3}+\frac{2}{3.5}+......+\frac{2}{13.15}+\frac{2}{15.17}\)
\(\Leftrightarrow A=1-\frac{1}{17}=\frac{16}{17}\)
\(\frac{\left(\frac{3}{15}+\frac{1}{4}+\frac{7}{20}\right)\times\frac{17}{49}}{5\frac{1}{3}+\frac{2}{5}}\)
\(=\frac{\left(\frac{12}{60}+\frac{15}{60}+\frac{21}{60}\right)\times\frac{17}{49}}{\frac{16}{3}\times\frac{2}{5}}\)
\(=\frac{\frac{48}{60}\times\frac{17}{49}}{\frac{80}{15}+\frac{6}{15}}\)
\(=\frac{\frac{816}{2940}}{\frac{86}{15}}\)
\(=\frac{816}{2940}:\frac{86}{15}\)
\(=\frac{816}{2940}\times\frac{15}{86}\)
\(=\frac{68}{245}\times\frac{15}{86}\)
\(=\frac{102}{2107}\)
1/1+2+1/1+2+3+1/1+2+3+4+1/1+2+3+4+5
=1/3+1/6+1/10+1/15
lấy mẫu số chung là 30,ta có:
10/30+5/6+3/10+2/30
=20/30=2/3
\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}...1\frac{1}{120}\)
\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}...\frac{121}{120}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{11.11}{10.12}\)
\(=\frac{2.3.4...11}{1.2.3...10}.\frac{2.3.4...11}{3.4.5...12}\)
\(=11.\frac{2}{12}=11.\frac{1}{6}=\frac{11}{6}\)