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A=(2+3+...+13)-(1+2+...+12)=2+3+...+13-1-2-...-12=(13-1)+(2-2)+(3-3)+...+(12-12)=12
\(\dfrac{-5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{4}{-9}+\dfrac{7}{15}\)
=\(\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}\)
=\(-1+1-\dfrac{2}{11}=\dfrac{-2}{11}\)
\(=\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)+\dfrac{-2}{11}\\ =-1+1+\dfrac{-2}{11}\\ =0+\dfrac{-2}{11}=\dfrac{-2}{11}\)
2.9 . 3/-11 + 2/9 . -8/11 + 1/3
= 2/9 . (3/-11 + -8/11) + 1/3
= 2/9 . (-1) + 1/3
= -2/9 + 1/3
= 1/9
3/5 . 7/8 - 3/5 . -1/5
= 3/8 . (7/8 - 1/5)
= 3/8 . 43/40
= 129/320
\(\frac{2}{9}\) x \(\frac{3}{-11}\) +\(\frac{2}{9}\) x\(\frac{-8}{11}\) +\(\frac{1}{3}\) =\(\frac{1}{9}\) \(\frac{3}{5}\) *\(\frac{7}{8}\) -\(\frac{3}{5}\)*\(\frac{-1}{5}\) =\(\frac{129}{200}\)
\(\dfrac{9}{2\cdot5}+\dfrac{9}{5\cdot8}+\dfrac{9}{8\cdot11}+...+\dfrac{9}{65\cdot68}\)
\(=\dfrac{3\cdot3}{2\cdot5}+\dfrac{3\cdot3}{5\cdot8}+\dfrac{3\cdot3}{8\cdot11}+...+\dfrac{3\cdot3}{65\cdot68}\)
\(=3\cdot\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{65}-\dfrac{1}{68}\right)\)
\(=3\cdot\left(\dfrac{1}{2}-\dfrac{1}{68}\right)\)
\(=3\cdot\left(\dfrac{34}{68}-\dfrac{1}{68}\right)\)
\(=3\cdot\dfrac{33}{68}\)
\(=\dfrac{99}{68}=4\dfrac{25}{68}\)
\(Chúc\) \(bạn\) \(học\) \(tốt\) .
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