7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8 - 17/8.9 + 19/9.10

= 3+4/3.4 - 4+5/4.5 + 5+6/5.6 - 6+7/6.7 + 7+8/7.8 - 8+9/8.9 + 9+10/9.10

=1/3 + 1/4 - 1/4 - 1/5 + 1/5 + 1/6 -1/6 - 1/7 +1/7 +1/8 - 1/8 - 1/9 + 1/9 + 1/10

=1/3 + 1/10=13/30

\(=\frac{6+1}{12}-\frac{10-1}{20}+\frac{10+1}{30}-\frac{14-1}{42}+\frac{14+1}{56}-\frac{18-1}{72}+\frac{18+1}{90}\)

=\(\frac{6}{12}+\frac{1}{12}-\frac{10}{20}+\frac{1}{20}+\frac{10}{30}+\frac{1}{30}-\frac{14}{42}+\frac{1}{42}+\frac{14}{56}+\frac{1}{56}-\frac{18}{72}+\frac{1}{72}+\frac{18}{90}+\frac{1}{90}\)

=\(\frac{1}{2}+\frac{1}{12}-\frac{1}{2}+\frac{1}{20}+\frac{1}{3}+\frac{1}{30}-\frac{1}{3}+\frac{1}{42}+\frac{1}{4}+\frac{1}{56}-\frac{1}{4}+\frac{1}{72}+\frac{1}{5}+\frac{1}{90}\)

\(=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{5}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{6}\)

\(=\frac{1}{3}-\frac{1}{10}+\frac{1}{5}\)

\(=\frac{10}{30}-\frac{3}{30}+\frac{6}{30}=\frac{13}{30}\)

\(\frac{7}{3.4}-\frac{9}{4.5}+\frac{11}{5.6}-\frac{13}{6.7}+\frac{15}{7.8}-\frac{17}{8.9}-\frac{19}{9.10}+\frac{21}{10.11}\)

\(=\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}-\frac{9+10}{9.10}+\frac{10+11}{10.11}\)

\(=\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+\frac{1}{6}-\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+\frac{1}{8}-\frac{1}{8}-\frac{1}{9}+\frac{1}{9}+\frac{1}{10}-\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{3}-\frac{1}{11}=\frac{8}{33}\)

đặt \(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)

ta có:

\(M=\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}\)

\(\Leftrightarrow M=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}\) \(\Leftrightarrow M=\dfrac{3}{3.4}+\dfrac{4}{3.4}-\dfrac{4}{4.5}-\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{6}{5.6}-\dfrac{6}{6.7}-\dfrac{7}{6.7}+\dfrac{7}{7.8}+\dfrac{8}{7.8}-\dfrac{8}{8.9}-\dfrac{9}{8.9}+\dfrac{9}{9.10}+\dfrac{10}{9.10}\) \(\Rightarrow M=\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{7}-\dfrac{1}{9}-\dfrac{1}{8}+\dfrac{1}{10}+\dfrac{1}{9}\) \(\Rightarrow M=\dfrac{1}{3}+\dfrac{1}{10}\)

\(\Rightarrow M=\dfrac{10}{30}+\dfrac{3}{30}\)

\(\Rightarrow M=\dfrac{13}{30}\)

vậy M = \(\dfrac{13}{30}\)

vậy \(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{13}{30}\)

\(\dfrac{7}{3.4}-\dfrac{9}{4.5}+\dfrac{11}{5.6}-\dfrac{13}{6.7}+\dfrac{15}{7.8}-\dfrac{17}{8.9}+\dfrac{19}{9.10}=\dfrac{3+4}{3.4}-\dfrac{4+5}{4.5}+\dfrac{5+6}{5.6}-\dfrac{6+7}{6.7}+\dfrac{7+8}{7.8}-\dfrac{8+9}{8.9}+\dfrac{9+10}{9.10}=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}=\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{7}{30}\)

bạn tìm 1 số để nhân cả tử cả mẫu ra để tử ra 1 so chung nha rồi tách thôi

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