\(1001\left(\frac{2}{12012}+\frac{74}{555555}-\frac{2}{13.7.11.5}\right)\)
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17 tháng 9 2020
\(=\left(-\frac{1}{2}-\frac{1}{9}-\frac{7}{18}\right)+\left(\frac{3}{5}+\frac{2}{7}+\frac{4}{35}\right)+\frac{1}{127}\)
\(=\left(-\frac{9}{18}-\frac{2}{18}-\frac{7}{18}\right)+\left(\frac{21}{35}+\frac{10}{35}+\frac{4}{35}\right)+\frac{1}{127}\)
\(=\left(-\frac{18}{18}\right)+\frac{35}{35}+\frac{1}{127}\)
\(=-1+1+\frac{1}{127}\)
\(=\frac{1}{127}\)
SA
21 tháng 6 2018
\(B=\left(\frac{2}{2.3}-1\right)\left(\frac{2}{3.4}-1\right)...\left(\frac{2}{2008.2009}-1\right)\)
\(B=\left(\frac{2}{2.3}-\frac{6}{2.3}\right)\left(\frac{2}{3.4}-\frac{12}{3.4}\right)...\left(\frac{2}{2008.2009}-\frac{2008.2009}{2008.2009}\right)\)
\(B=\left(-\frac{4}{2.3}\right)\left(-\frac{10}{3.4}\right)...\left(\frac{2-2008.2009}{2008.2009}\right)\)
\(B=\left(-\frac{1.4}{2.3}\right)\left(-\frac{2.5}{3.4}\right)...\left(-\frac{2007.2010}{2008.2009}\right)\)
Biểu thức B có (2008 - 2) : 1 + 1 = 2007 (thừa số)
Vì cả 2007 thừa số của biểu thức B đều mang dấu (-)
Nên biểu thức B mang dấu (-)
\(B=-\frac{1.2....2007}{2.3...2008}.\frac{4.5...2010}{3.4...2009}\)
\(B=-\frac{1}{2008}.\frac{2010}{3}\)
\(B=-\frac{1.2010}{2008.3}=-\frac{1.1005}{1004.3}=-\frac{1.335}{1004.1}\)
\(B=-\frac{335}{1004}\)
Vậy\(B=-\frac{335}{1004}\)
MS
16 tháng 3 2017
\(\frac{\frac{2}{3}+\frac{2}{5}-\frac{2}{9}}{\frac{4}{3}+\frac{4}{5}-\frac{4}{9}}\) _ \(\frac{3-\frac{3}{11}-\frac{3}{17}}{5-\frac{5}{11}-\frac{5}{17}}\)
=\(\frac{2\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)}{4\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{9}\right)}\)_ \(\frac{3\left(1-\frac{1}{11}-\frac{1}{17}\right)}{5\left(1-\frac{1}{11}-\frac{1}{17}\right)}\)= \(\frac{2}{4}-\frac{3}{5}\)= \(\frac{-1}{10}\)
NN
17 tháng 9 2020
\(\frac{3}{5}+\frac{3}{11}-\left(\frac{-3}{7}\right)+\frac{2}{97}-\frac{1}{35}-\frac{3}{4}+\left(\frac{-23}{44}\right)\)
\(=\frac{3}{5}+\frac{3}{11}+\frac{3}{7}+\frac{2}{97}-\frac{1}{35}-\frac{3}{4}-\frac{23}{44}\)
\(=\left(\frac{3}{5}+\frac{3}{7}-\frac{1}{35}\right)+\left(\frac{3}{11}-\frac{3}{4}-\frac{23}{44}\right)+\frac{2}{97}\)
\(=\left(\frac{21}{35}+\frac{15}{35}-\frac{1}{35}\right)+\left(\frac{12}{44}-\frac{33}{44}-\frac{23}{44}\right)+\frac{2}{97}\)
\(=\frac{35}{35}+\left(\frac{-44}{44}\right)+\frac{2}{97}=1+\left(-1\right)+\frac{2}{97}=\frac{2}{97}\)
17 tháng 9 2020
\(=\left(\frac{3}{5}+\frac{3}{7}-\frac{1}{35}\right)+\left(\frac{3}{11}-\frac{3}{4}-\frac{23}{44}\right)+\frac{2}{97}\)
\(=\left(\frac{21}{35}+\frac{15}{35}-\frac{1}{35}\right)+\left(\frac{12}{44}-\frac{33}{44}-\frac{23}{44}\right)+\frac{2}{97}\)
\(=-1+1+\frac{2}{97}\)
\(=\frac{2}{97}\)
S
26 tháng 2 2017
\(\left(-1-\frac{1}{12}\right).\left(-1-\frac{1}{13}\right).\left(-1-\frac{1}{14}\right)...\left(-1-\frac{1}{2017}\right)\)
\(=\frac{-13}{12}.\frac{-14}{13}.\frac{-15}{14}...\frac{-2018}{2017}\)
\(=\frac{-13}{12}.\frac{14}{-13}.\frac{-15}{14}...\frac{2018}{-2017}\)
\(=\frac{\left(-13\right).14.\left(-15\right)...2018}{12.\left(-13\right).14...2017}=\frac{2018}{12}=\frac{1009}{6}\)
\(1001\left(\frac{2}{12012}+\frac{74}{555555}-\frac{2}{13.7.11.5}\right)=\frac{1001.2}{12012}+\frac{1001.74}{555555}-\frac{1001.2}{13.11.7.5}=\frac{1001.2}{12.1001}+\frac{1001.2.37}{1001.37.15}-\frac{1001.2}{1001.5}\)\(=\frac{1}{6}+\frac{2}{15}-\frac{2}{5}=\frac{5}{30}+\frac{4}{30}-\frac{12}{30}=-\frac{3}{30}=-\frac{1}{10}\)
\(1001\left(\frac{2}{12012}+\frac{74}{555555}-\frac{2}{13.7.77.5}\right)=\frac{1001.2}{12.1001}+\frac{1001.74}{555.1001}-\frac{1001.2}{85.1001}=\frac{1}{6}+\frac{74}{555}-\frac{2}{85}=11877\)