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A=5.(2.3+4.9.5+6.9.7+10.21.8)/7.(2.3+4.9.5+6.9.7+10.21.8)
A=5/7
A = \(\dfrac{2.3.5+4.9.35+6.9.35+10.21.40}{2.3.7+4.9.35+6.9.49+10.21.56}\)
A = \(\dfrac{2.3.5+\left(2.3.5\right).2.3.5+\left(2.3.5\right).3.3.7+\left(2.3.5\right).5.7.8}{2.3.7+\left(2.3.7\right).2.3.5+\left(2.3.7\right).3.3.7+\left(2.3.7\right).5.7.8}\)
A = \(\dfrac{2.3.5.\left(1+2.3.5+3.3.7+5.7.8\right)}{2.3.7\left(1+2.3.5+3.3.7+5.7.8\right)}\)
A = \(\dfrac{2.3.5}{2.3.7}\)
A = \(\dfrac{5}{7}\)
Ta có: \(A=\dfrac{2\cdot3\cdot5+4\cdot9\cdot35+6\cdot9\cdot35+10\cdot21\cdot40}{2\cdot3\cdot7+4\cdot9\cdot35+6\cdot9\cdot49+10\cdot21\cdot56}\)
\(=\dfrac{2\cdot3\cdot5+2\cdot3\cdot5\cdot6\cdot7+2\cdot3\cdot5\cdot3\cdot3\cdot7+2\cdot3\cdot5\cdot5\cdot7\cdot8}{2\cdot3\cdot7+2\cdot3\cdot7\cdot2\cdot3\cdot5+2\cdot3\cdot7\cdot3\cdot3\cdot7+2\cdot3\cdot7\cdot5\cdot7\cdot8}\)
\(=\dfrac{2\cdot3\cdot5\cdot\left(1+2\cdot3\cdot7+3\cdot3\cdot7+5\cdot7\cdot8\right)}{2\cdot3\cdot7\cdot\left(1+2\cdot3\cdot5+3\cdot3\cdot7+5\cdot7\cdot8\right)}\)
\(=\dfrac{5}{7}\cdot\dfrac{386}{374}=\dfrac{965}{1309}\)
\(A=5\left(1+5\right)+...+5^{11}\left(1+5\right)\)
\(=6\cdot\left(5+...+5^{11}\right)⋮30\)
2.2.5 < 2.3.53
vì 2.5 = 2.5 và 2 < 3