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\(\Rightarrow A=\frac{14}{15}.\frac{20}{21}.\frac{41}{42}.....\frac{209}{210}\)
\(=\frac{4.7}{5.6}.\frac{5.8}{6.7}.\frac{6.9}{7.8}.....\frac{19.22}{20.21}\)
\(=\frac{22}{6}=\frac{11}{3}\)
xin loi nhung ma minh cung dang khong giai duoc cau nay, minh mong cac ban tren Online Math giup minh nhe
\(A=\left(1-\frac{1}{15}\right).\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right)......\left(1-\frac{1}{1275}\right)\)
C=2/3.5/6.9/10...209/210
C=4/6.10/12.18/20...418/420 là do nhân với 2
C=1.4/2.3.2.5/3.4.3.6/4.5...19.22/20.21
C=1.2.3....19/2.3.4...20.4.5.6...22/3.4.5...21
C=1/20.22/3
C=11/30
Dễ ấy mà hiểu chưa
\(A=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}....\frac{1325}{1326}=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}....\frac{2650}{2652}\)
\(A=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}....\frac{50.53}{51.52}=\frac{\left(5.6.7...50\right).\left(8.9.10...53\right)}{\left(6.7.8...51\right).\left(7.8.9...52\right)}=\frac{5.53}{51.7}=..\)
\(C=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{210}\right)\)
\(C=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{209}{210}\)
\(C=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{418}{420}\)
\(C=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{19.22}{20.21}\)
\(C=\frac{1.4.2.5.3.6.4.7...19.22}{2.3.3.4.4.5.5.6...20.21}\)
\(C=\frac{\left(1.2.3.4...19\right).\left(4.5.6.7...22\right)}{\left(2.3.4.5...20\right).\left(3.4.5.6...21\right)}\)
\(C=\frac{1.22}{20.3}=\frac{1.11}{10.3}=\frac{11}{30}\)
\(A=\frac{14}{15}.\frac{20}{21}.\frac{27}{28}....\frac{209}{210}=\frac{28}{30}.\frac{40}{42}.\frac{54}{56}....\frac{418}{420}=\frac{4.7}{5.6}.\frac{5.8}{6.7}.\frac{6.9}{7.8}....\frac{19.22}{20.21}\)
\(=\frac{4.5.6...19}{5.6.7...20}.\frac{7.8.9...22}{6.7.8...21}=\frac{4}{20}.\frac{22}{6}=\frac{11}{5}\)