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3 tháng 8 2017
\(\left(1-\frac{1}{21}\right)\cdot\left(1-\frac{1}{28}\right)\cdot\left(1-\frac{1}{36}\right)\cdot...\cdot\left(1-\frac{1}{1326}\right)\)
\(=\frac{20}{21}\cdot\frac{27}{28}\cdot\frac{35}{36}\cdot...\cdot\frac{1325}{1326}\)
\(=\frac{40}{42}\cdot\frac{54}{56}\cdot\frac{70}{72}\cdot...\cdot\frac{2650}{2652}\)
\(=\frac{5.8}{6.7}\cdot\frac{6.9}{7.8}\cdot\frac{7.10}{8.9}\cdot....\cdot\frac{50.53}{51.52}\)
\(=\frac{5\cdot6\cdot7\cdot.....\cdot50}{6\cdot7\cdot8\cdot....\cdot51}\cdot\frac{8\cdot9\cdot10\cdot....\cdot53}{7\cdot8\cdot9\cdot...\cdot52}=\frac{5}{51}\cdot\frac{53}{7}=\frac{265}{357}\)
15 tháng 7 2018
\(\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)\left(1-\frac{1}{36}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{1}{1326}\right)\)
\(=\frac{20}{21}\cdot\frac{27}{28}\cdot\frac{35}{36}\cdot\cdot\cdot\cdot\cdot\frac{1325}{1326}\)
\(=\frac{40}{42}\cdot\frac{54}{56}\cdot\frac{70}{72}\cdot\cdot\cdot\cdot\cdot\cdot\frac{2650}{2652}\)
\(=\frac{5\cdot8}{6\cdot7}\cdot\frac{6\cdot9}{7\cdot8}\cdot\frac{7\cdot10}{8\cdot9}\cdot\cdot\cdot\cdot\cdot\frac{50\cdot53}{51\cdot52}\)
\(=\frac{\left(5\cdot8\right)\left(6\cdot9\right)\left(7\cdot10\right)\cdot\cdot\cdot\cdot\cdot\left(50\cdot53\right)}{\left(6\cdot7\right)\left(7\cdot8\right)\left(8\cdot9\right).....\left(51\cdot52\right)}\)
\(=\frac{\left(5\cdot6\cdot7\cdot\cdot\cdot\cdot\cdot50\right)\cdot\left(8\cdot9\cdot10\cdot\cdot\cdot\cdot\cdot53\right)}{\left(6\cdot7\cdot8\cdot\cdot\cdot\cdot\cdot51\right)\cdot\left(7\cdot8\cdot9\cdot\cdot\cdot\cdot\cdot52\right)}\)
\(=\frac{5\cdot53}{51\cdot7}=\frac{265}{357}\)
29 tháng 6 2015
\(A=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}....\frac{1325}{1326}=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}....\frac{2650}{2652}\)
\(A=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}....\frac{50.53}{51.52}=\frac{\left(5.6.7...50\right).\left(8.9.10...53\right)}{\left(6.7.8...51\right).\left(7.8.9...52\right)}=\frac{5.53}{51.7}=..\)
6 tháng 7 2016
\(\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right).\left(1-\frac{1}{36}\right)...\left(1-\frac{1}{1326}\right)\)
\(=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}...\frac{1325}{1326}\)
\(=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}...\frac{2650}{2652}\)
\(=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}...\frac{50.53}{51.52}\)
\(=\frac{5.6.7...50}{7.8.9...52}.\frac{8.9.10...53}{6.7.8...51}\)
\(=\frac{5.6}{51.52}.\frac{52.53}{6.7}\)
\(=\frac{5.52}{51.7}=\frac{260}{357}\)
Ủng hộ mk nha ^_-
14 tháng 8 2016
Câu hỏi của Nguyễn Minh Tuấn - Toán lớp 6 - Học toán với OnlineMath
\(A=\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right).\left(1-\frac{1}{36}\right)...\left(1-\frac{1}{1326}\right)\)
\(A=\frac{20}{21}.\frac{27}{28}.\frac{35}{36}...\frac{1325}{1326}\)
\(A=\frac{40}{42}.\frac{54}{56}.\frac{70}{72}...\frac{2650}{2652}\)
\(A=\frac{5.8}{6.7}.\frac{6.9}{7.8}.\frac{7.10}{8.9}...\frac{50.53}{51.52}\)
\(A=\frac{5.6.7...50}{6.7.8...51}.\frac{8.9.10...53}{7.8.9...52}\)
\(A=\frac{5}{51}.\frac{53}{7}\)
\(A=\frac{265}{357}\)