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a) \(\frac{30}{51}\)\(-\)\(\frac{20}{52}\)\(+\)\(\frac{14}{34}-\frac{56}{91}-2\)
\(=\frac{10}{17}-\frac{5}{13}+\frac{7}{17}-\frac{8}{13}-2\)
= (\(\frac{10}{17}\)\(+\frac{7}{17}\)) \(-\)(\(\frac{5}{13}+\frac{8}{13}\)) \(-2\)
= \(1-1-2\)
=\(0-2\)
= -2
k cho mik nha
\(\frac{22}{45}\)< \(\frac{51}{101}\)
\(\frac{23}{48}\)< \(\frac{47}{92}\)
\(\frac{34}{43}\)< \(\frac{35}{42}\)
\(60!=1\cdot2\cdot3\cdot4\cdot5\cdot...\cdot59\cdot60=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2\cdot4\cdot6\cdot...\cdot58\cdot60\)
\(=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2^{30}\cdot1\cdot2\cdot3\cdot...\cdot30=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2^{30}\times30!\)
\(\Rightarrow1\cdot3\cdot5\cdot...\cdot59=\frac{60!}{30!\times2^{30}}=\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}\)đpcm.
\(\frac{31}{2}\cdot\frac{32}{2}\cdot...\cdot\frac{60}{2}\cdot2\cdot4\cdot...\cdot58\cdot60\)
=31.32.33.34...60.1.2.3.4.5...29.30
=1.2.3.4.5.6.7.8.9.10...60
1.3.5.7...59.2.4.6.8...60
=1.2.3.4.5.6...60
Vậy \(\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}=1\cdot3\cdot5\cdot...\cdot59\)