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\(-\left(\frac{3}{10}-\frac{6}{11}\right)-\left(\frac{21}{30}-\frac{5}{11}\right)-\left(-\frac{1}{2}+20\%\right)\)
\(=-\frac{3}{10}+\frac{6}{11}-\frac{21}{30}+\frac{5}{11}+\frac{1}{2}+\frac{20}{100}\)
\(=-\frac{3}{10}-\frac{7}{10}+\frac{6}{11}+\frac{5}{11}+\frac{1}{2}+\frac{1}{5}\)
\(=-1+1+\frac{7}{10}\)
\(=\frac{7}{10}\)
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\(\dfrac{21}{36}-\left(-\dfrac{11}{30}\right)=\dfrac{7}{12}+\dfrac{11}{30}=\dfrac{7.5+11.2}{60}=\dfrac{57}{60}=\dfrac{19}{20}\\ ----\\\dfrac{-4}{8}+\left(-\dfrac{3}{10}\right)=\dfrac{-1}{2}-\dfrac{3}{10}=\dfrac{-1.5-3}{10}=\dfrac{-8}{10}=-\dfrac{4}{5}\\ ----\\ \dfrac{7}{12}-\left(-\dfrac{9}{20}\right)=\dfrac{7}{12}+\dfrac{9}{20}=\dfrac{7.5+9.3}{60}=\dfrac{62}{60}=\dfrac{31}{30}\\ ---\\ \dfrac{-2}{5}+\left(-\dfrac{11}{30}\right)=-\dfrac{2}{5}-\dfrac{11}{30}=\dfrac{-2.6-11}{30}=-\dfrac{29}{30}\)
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S = 1 + 31 + 32 + 33 + ... + 330
3S = 3 + 32 + 33 + 34 + ... + 331
3S - S = (3 + 32 + 33 + 34 + ... + 331) - (1 + 31 + 32 + 33 + ... + 330)
2S = 331 - 1
\(S=\frac{3^{31}-1}{2}\)
Gọi A= 1+ 2+ 3+...+ 30+ 31.
Dãy A có số các số hạng là:
( 31- 1): 1+ 1= 31( số)
Tổng dãy A là:
( 31+ 1)x 31: 2= 496.
Vậy 1+ 2+ 3+...+ 30+ 31= 496.
\(\left(31-1+1\right).\left(31+1\right):2\)
\(=31.32:2\)
\(496\)