\(\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{2\text{x}3+4\text{x}6+6\text{x}9+8\text{x}12}\)
\(=\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{\text{1x}2\text{x}3+2\text{x}4\text{x}3+3\text{x}6\text{x}3+4\text{x}8\text{x}3}\)
\(=\frac{1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8}{3\left(1\text{x}2+2\text{x}4+3\text{x}6+4\text{x}8\right)}\)
\(=\frac{1}{3}\)
Ta có: \(\frac{1.2+2.4+3.6+4.8}{2.3+4.6+6.9+8.12}=\frac{1.2}{2.3}+\frac{2.4}{4.6}+\frac{3.6}{6.9}+\frac{4.8}{8.12}.\)
\(=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{1}{3}.4=\frac{4}{3}\)
1x2 + 2x4 + 3x6 + 4x8
= (1x2) (1 + 2 + 3 + 4) 2x3 + 4x6 + 6x9 + 8x12
= (2x3) (1 + 2 + 3 + 4)
Do đó, (1x2 + 2x4 + 3x6 + 4x8 ) / (2x3 + 4x6 + 6x9 + 8x12)
= (1x2) / (2x3) = 1/3
