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20 tháng 12 2015
\(\frac{-1}{2}-\frac{1}{3}-\frac{1}{4}-.........-\frac{1}{20}+\frac{3}{2}+\frac{4}{3}+\frac{5}{4}+...........+\frac{21}{20}\)
=\(\left(\frac{-1}{2}+\frac{3}{2}\right)+\left(\frac{-1}{3}+\frac{4}{3}\right)+\left(\frac{-1}{4}+\frac{5}{4}\right)+..................+\left(\frac{-1}{20}+\frac{21}{20}\right)\)
=\(1+1+1+.........+1\)(19 số 1)
=19
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
21 tháng 7 2023
\(A=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+...+\dfrac{1}{18.19.20}\)
\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{20-18}{18.19.20}=\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{18.19}-\dfrac{1}{19.20}=\dfrac{1}{2}-\dfrac{1}{19.20}\)
\(\Rightarrow A=\left(\dfrac{1}{2}-\dfrac{1}{19.20}\right):2\)
16 tháng 6 2016
*\(\frac{\left(\frac{3}{10}-\frac{4}{15}-\frac{7}{20}\right).\frac{5}{19}}{\left[\frac{1}{14}+\frac{1}{7}-\left(-\frac{3}{35}\right)\right].\frac{4}{3}}=\frac{\left(\frac{18}{60}-\frac{16}{60}-\frac{21}{60}\right).\frac{5}{19}}{\left(\frac{5}{70}+\frac{10}{70}+\frac{6}{70}\right).\frac{4}{3}}=\frac{\frac{-19}{60}.\frac{5}{19}}{\frac{21}{70}.\frac{4}{3}}=\frac{\frac{-1}{12}}{\frac{14}{35}}=-\frac{1}{12}.\frac{35}{14}=\frac{-35}{168}\)
*\(\frac{\left(1+2+3+...+100\right).\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
=\(\frac{\left(1+2+3+...+100\right)\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(\frac{63}{10}.12-21.\frac{18}{5}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
=\(\frac{\left(1+2+3+...+100\right)\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).\left(\frac{378}{5}-\frac{378}{5}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
=\(\frac{\left(1+2+3+...+100\right)\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-\frac{1}{9}\right).0}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}=0\)
\(\frac{1}{2}.3+\frac{1}{3}.4+...+\frac{1}{19}.20\)
\(=\frac{3}{2}.\frac{4}{3}......\frac{20}{19}\)
\(=\frac{3.4.5....20}{2.3.4...19}\)
\(=\frac{20}{2}=10\)
\(\frac{1}{2}\times3+\frac{1}{3}\times4+\frac{1}{4}\times5+...+\frac{1}{19}\times20\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{20}{19}\)
\(=\frac{3\times4\times5\times...\times20}{2\times3\times4\times...\times19}\)
\(=\frac{20}{2}\)
\(=10\)