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LA
2
24 tháng 4 2015
a)\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{5\cdot6}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\left(1-\frac{1}{6}\right)+\left(\frac{1}{2}-\frac{1}{2}\right)+...+\left(\frac{1}{5}-\frac{1}{5}\right)\)
\(=\left(1-\frac{1}{6}\right)+0+...+0=1-\frac{1}{6}=\frac{6}{6}-\frac{1}{6}=\frac{5}{6}\)
b)\(\frac{3}{2\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}\)
\(=\left(\frac{1}{2}-\frac{1}{14}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+\left(\frac{1}{11}-\frac{1}{11}\right)\)
\(=\left(\frac{1}{2}-\frac{1}{14}\right)+0+...+0=\frac{1}{2}-\frac{1}{14}=\frac{7}{14}-\frac{1}{14}=\frac{6}{14}\)
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M
26 tháng 9 2017
\(1+2+3+...+2005+2006=\left[\left(2006-1\right):1+1\right].\left(2006+1\right):2.\)
\(=2006.2007:2\)
\(=2013021\)
\(5+10+...+2000+2005=\left[\left(2005-5\right):5+1\right].\left(2005+5\right):2.\)
\(=401.2010:2\)
\(=403005\)
\(140+136+....+64+60=\left[\left(140-60\right):16+1\right].\left(140+60\right):2.\)
\(=6.200:2\)
\(=600\)
KN
2
2 tháng 4 2016
=(3/2-9/10)+(5/6-17/42)+(7/12-13/4)+11/30-15/56
=3/5+37+(-29/12)+11/30-15/56
=29/30+39/56+29/12
=227/840
NHỚ K MÌNH NHA
5 tháng 1 2016
1) = 0 + 10 - 50 = -40
2) = 0 + 71 + 15 = 86
3) = 0 + 71 + 18 = 89
4) = 30 - 0 - 85 = -55
VM
4
Y
13 tháng 6 2023
\(\left(\dfrac{1}{3}-\dfrac{3}{10}\right):\dfrac{3}{5}+\left(\dfrac{2}{3}-\dfrac{7}{10}\right):\dfrac{3}{5}\)
\(=\left(\dfrac{1.10}{3.10}-\dfrac{3.3}{10.3}\right).\dfrac{5}{3}+\left(\dfrac{2.10}{3.10}-\dfrac{7.3}{10.3}\right).\dfrac{5}{3}\)
\(=\left(\dfrac{10}{30}-\dfrac{9}{30}\right).\dfrac{5}{3}+\left(\dfrac{20}{30}-\dfrac{21}{30}\right).\dfrac{5}{3}\)
\(=\dfrac{1}{30}.\dfrac{5}{3}-\dfrac{1}{30}.\dfrac{5}{3}\)
\(=\dfrac{5}{3}.\left(\dfrac{1}{30}-\dfrac{1}{30}\right)\)
\(=\dfrac{5}{3}.0\)
\(=0\)
KT
3
N
24 tháng 6 2019
\(a)-\left(\frac{3}{10}-\frac{6}{11}\right)-\left(\frac{21}{30}-\frac{5}{11}\right)\)
\(=-\frac{3}{10}+\frac{6}{11}-\frac{21}{30}+\frac{5}{11}\)
\(=\left(-\frac{3}{10}-\frac{21}{30}\right)+\left(\frac{6}{11}+\frac{5}{11}\right)\)
\(=-1+1\)
\(=0\)
\(b)\left(\frac{13}{5}+\frac{7}{16}\right)-\left(\frac{11}{16}-\frac{12}{10}\right)\)
\(=\frac{13}{5}+\frac{7}{16}-\frac{11}{16}+\frac{12}{10}\)
\(=\left(\frac{13}{5}+\frac{12}{10}\right)+\left(\frac{7}{16}-\frac{11}{16}\right)\)
\(=\frac{19}{5}+\left(-\frac{1}{4}\right)\)
\(=\frac{71}{20}\)
24 tháng 6 2019
a) \(-\left(\frac{3}{10}-\frac{6}{11}\right)-\left(\frac{21}{30}-\frac{5}{11}\right)\)
\(=\frac{-3}{10}+\frac{6}{11}-\frac{21}{30}+\frac{5}{11}\)
\(=\left(\frac{-3}{10}-\frac{21}{30}\right)+\left(\frac{6}{11}+\frac{5}{11}\right)\)
\(=\left(\frac{-9}{30}-\frac{21}{30}\right)+1\)
\(=-1+1\)
= 0
b) \(\left(\frac{13}{5}+\frac{7}{16}\right)-\left(\frac{11}{16}-\frac{12}{10}\right)\)
\(=\frac{13}{5}+\frac{7}{16}-\frac{11}{16}+\frac{12}{10}\)
\(=\left(\frac{13}{5}+\frac{12}{10}\right)+\left(\frac{7}{16}-\frac{11}{16}\right)\)
\(=\left(\frac{26}{10}+\frac{12}{10}\right)-4\)
= \(\frac{19}{5}-4\)
= \(\frac{-1}{5}\)
=3.(10+60+30)
=3.100
=300