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\(\frac{10}{11}:\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{10}{11}:\frac{8}{33}=\frac{10}{11}.\frac{33}{8}\)
\(=\frac{15}{4}\)
Trả lời:
\(\frac{10}{11}\div\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{10}{11}\div\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{10}{11}\div\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{10}{11}\div\frac{8}{33}\)
\(=\frac{10}{11}\times\frac{33}{8}\)
\(=\frac{15}{4}\)
\(\frac{10}{11}:\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{10}{11}:\left(\frac{11}{33}-\frac{3}{33}\right)\)
\(=\frac{10}{11}:\frac{8}{33}\)
\(=\frac{15}{4}\)
Học tốt
\(\frac{10}{11}:\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\right)\)
\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{10}{11}:\left(\frac{1}{3}-\frac{1}{11}\right)\)
\(=\frac{10}{11}:\frac{8}{33}\)
\(=\frac{10}{11}.\frac{33}{8}\)
\(=\frac{15}{4}\)
\(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)
\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(A=\frac{1}{2}-\frac{1}{8}=\frac{3}{8}\)
\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\\ \)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}\)
\(=\frac{4}{8}-\frac{1}{8}\\ =\frac{3}{8}\)
Chúc bn học thiệt giỏi nhé!
\(\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{19.21}\right).x=\frac{9}{7}\)
\(\left(\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{21-19}{19.21}\right).x=\frac{9}{7}\)
\(\left[\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\right].x=\frac{9}{7}\)
\(\left[\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\right].x=\frac{9}{7}\)
\(\left[\frac{1}{2}.\frac{2}{7}\right].x=\frac{9}{7}\)
\(\frac{1}{7}.x=\frac{9}{7}\)
\(\Rightarrow x=\frac{9}{7}\div\frac{1}{7}=9\)
\(\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)x=\frac{9}{7}\)
\(\Leftrightarrow\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)x=\frac{9}{7}\)
\(\Leftrightarrow\left(\frac{1}{3}-\frac{1}{21}\right)x=\frac{9}{7}\)
\(\Leftrightarrow\frac{2}{7}x=\frac{9}{7}\)
\(\Leftrightarrow x=\frac{9}{2}\)
\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(S=1-\frac{1}{9}=\frac{8}{9}\)
Mình sửa lại đề xíu.
a) \(\frac{75}{100}+\frac{18}{21}+\frac{19}{32}+\frac{1}{4}+\frac{3}{21}+\frac{13}{32}=\frac{3}{4}+\frac{1}{4}+\frac{18}{21}+\frac{3}{21}+\frac{19}{32}+\frac{13}{32}=1+1+1=3\)
b) \(4\frac{2}{5}+5\frac{6}{9}+2\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}=4+\frac{2}{5}+\frac{3}{5}+5+\frac{2}{3}+\frac{1}{3}+2+\frac{3}{4}+\frac{1}{4}\)
\(=4+1+5+1+2+1=14.\)
c) \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{41\cdot43}=\frac{5-3}{3\cdot5}+\frac{7-5}{5\cdot7}+\frac{9-7}{7\cdot9}+...+\frac{43-41}{41\cdot43}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{41}-\frac{1}{43}=\frac{1}{3}-\frac{1}{43}=\frac{43-3}{3\cdot43}=\frac{40}{129}.\)