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\(D=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)
\(D=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}\)
\(D=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}\)
\(D=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{38.41}{39.40}\)
\(D=\frac{1.2.3.4...38}{3.4.5.6...40}.\frac{4.5.6.7...41}{2.3.4.5...39}\)
\(D=\frac{2}{39.40}.\frac{40.41}{2.3}\)
\(D=\frac{41}{39.3}=\frac{41}{117}\)
A=(−2/3 ).(−5/6 ).(−9/10 )...(−779/780 )=(−4/6 ).(−10/12 ).(−18/20 )....(−1558/1560 )
A=(−1.4).(−2.5).(−3.6)....(−38.41) / (2.3).(3.4).(4.5)....(39.40) =(1.2.3....38).(4.5.6...41) / (2.3.4...39).(3.4.5...40) ( Vì từ -1 đến -38 có 38 số =>tích của 38 số âm = tích của 38 số dương)
A=(1.2.3....38).(4.5.6...41) / (2.3.4...39).(3.4.5...40) =1.41/39.3 =41/ 117
a) \(\frac{1}{3}.\frac{-6}{13}.\frac{-9}{10}.\frac{-13}{36}\)
\(=\left(\frac{1}{3}.\frac{-9}{10}\right)\left(\frac{-6}{13}.\frac{-13}{36}\right)\)
\(=\frac{-3}{10}.\frac{1}{6}\)
\(=\frac{-1}{20}\)
b) \(\frac{-1}{3}.\frac{-15}{17}.\frac{34}{45}\)
\(=\frac{-1}{3}.\frac{-2}{3}\)
\(=\frac{2}{9}\)
c) \(\left(1-\frac{1}{5}\right)\left(\frac{-3}{10}+\frac{1}{5}\right)\)
\(=\frac{4}{5}.\frac{-1}{10}\)
\(=\frac{-2}{25}\)
d) \(A=\frac{1}{3}.\frac{4}{5}+\frac{1}{3}.\frac{6}{5}+\frac{2}{3}\)
\(=\frac{1}{3}\left(\frac{4}{5}+\frac{6}{5}\right)+\frac{2}{3}\)
\(=\frac{1}{3}.2+\frac{2}{3}\)
\(=\frac{2}{3}+\frac{2}{3}\)
\(=\frac{4}{3}\)
e) \(11\frac{1}{4}-\left(2\frac{5}{7}+5\frac{1}{4}\right)\)
\(=\left(11\frac{1}{4}-5\frac{1}{4}\right)-2\frac{5}{7}\)
\(=6-2\frac{5}{7}\)
\(=5\frac{7}{7}-2\frac{5}{7}\)
\(=3\frac{2}{7}\)
\(\left(\frac{1}{2\times3}+\frac{2}{3\times5}+\frac{3}{5\times8}+\frac{4}{8\times12}\right)\div5\)
\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{12}\right)\div5\)
\(=\left(\frac{1}{2}-\frac{1}{12}\right)\div5\)
\(=\frac{5}{12}\div5\)
\(=\frac{1}{12}\)
\(\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right):5\)
= \(\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right):5\)
\(=\left(\frac{20}{120}+\frac{16}{120}+\frac{9}{120}+\frac{5}{120}\right):5\)
\(=\frac{50}{120}:5\)
\(=\frac{5}{12}:5\)
\(=\frac{1}{12}\)