Tính nhanh: \(1-\frac56+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}\)
K
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27 tháng 1 2022
\(M=\left(\dfrac{3}{2}-\dfrac{5}{6}+\dfrac{7}{12}-\dfrac{17}{72}\right)+\left(-\dfrac{9}{20}+\dfrac{11}{30}\right)+\left(\dfrac{-13}{42}+\dfrac{15}{56}\right)\)
\(=\dfrac{108}{72}-\dfrac{60}{72}+\dfrac{42}{72}-\dfrac{17}{72}+\dfrac{-27}{60}+\dfrac{22}{60}+\dfrac{-52}{168}+\dfrac{45}{168}\)
\(=\dfrac{73}{72}-\dfrac{1}{12}-\dfrac{1}{24}=\dfrac{73}{72}-\dfrac{6}{72}-\dfrac{3}{72}=\dfrac{64}{72}=\dfrac{8}{9}\)
D
29 tháng 2 2016
ta có: \(1-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(=1-\frac{5}{2.3}+\frac{7}{3.4}-\frac{9}{4.5}+\frac{11}{5.6}-\frac{13}{6.7}+\frac{15}{7.8}-\frac{17}{8.9}+\frac{19}{9.10}\)
\(=1-\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+\frac{1}{8}-\frac{1}{8}+\frac{1}{9}-\frac{1}{9}+\frac{1}{10}\)
\(=1-\frac{1}{2}+\frac{1}{10}=\frac{3}{5}\)
AK
30 tháng 4 2018
\(S=\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{42}\)
\(=1+\frac{1}{2}-\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+\frac{1}{4}-\frac{1}{4}-\frac{1}{5}+\frac{1}{5}\)+ \(\frac{1}{6}-\frac{1}{6}-\frac{1}{7}+\frac{1}{7}\)+ \(\frac{1}{8}-\frac{1}{8}-\frac{1}{9}\)
\(=1-\frac{1}{9}\)
\(=\frac{9}{9}-\frac{1}{9}\)
\(=\frac{8}{9}\)
Chúc bạn học tốt !!!
Ta có: \(1-\frac56+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}\)
\(=1-\frac{2+3}{2\times3}+\frac{3+4}{3\times4}-\frac{4+5}{4\times5}+\frac{5+6}{5\times6}-\frac{6+7}{6\times7}+\frac{7+8}{7\times8}\)
\(=1-\frac12-\frac13+\frac13+\frac14-\frac14-\frac15+\frac15+\frac16-\frac16-\frac17+\frac17+\frac18\)
\(=1+\frac18=\frac98\)