\(\dfrac{1.2.3+2.4.6+4.8.12+7.14.21}{1.3.6+2.6.12+4.12.24+7.21.42}\)
\(=\dfrac{1.2.3\left(1+2.2.2+4.4.4+7.7.7\right)}{1.3.6\left(1+2.2.2+4.4.4+7.7.7\right)}\)
\(=\dfrac{1.2.3}{1.3.6}=\dfrac{1}{3}\)
Ta có:
\(\dfrac{1.2.3+2.4.6+4.8.12+7.14.21}{1.3.6+2.6.12+4.12.24+7.21.41}\)
=\(\dfrac{1.2.3\left(1+2^3+4^3+7^3\right)}{1.3.6\left(1+2^3+4^3+7^3\right)}\)= \(\dfrac{1.2.3}{1.3.6}\) = \(\dfrac{1}{3}\)
\(\dfrac{1\cdot2\cdot3+2\cdot4\cdot6+4\cdot8\cdot12+7\cdot14\cdot21}{1\cdot3\cdot6+2\cdot6\cdot12+4\cdot12\cdot24+7\cdot21\cdot42}\)
\(=\dfrac{1\cdot2\cdot3\left(1+2\cdot2\cdot2+4\cdot4\cdot4+7\cdot7\cdot7\right)}{1\cdot3\cdot6\left(1+2\cdot2\cdot2+4\cdot4\cdot4+7\cdot7\cdot7\right)}\)
\(=\dfrac{1\cdot2\cdot3}{1\cdot3\cdot6}\)
\(=\dfrac{1}{3}\)
\(\dfrac{1.2.3+2.4.6+4.8.12+7.14.21}{1.3.6+2.6.12+4.12.24+7.12.21}\\ =\dfrac{1.2.3\left(1.1.1+2.2.2+3.3.3+4.4.4+7.7.7\right)}{1.3.6\left(1.1.1+2.2.2+3.3.3+4.4.4+7.7.7\right)}\\ =\dfrac{1.2.3}{1.3.6}=\dfrac{1}{3}\)
