\(\frac{1.2.3+2.4.6+4.8.12+7.14.21}{1.3.5+2.6.10+4.12.30+7.21.35}\)
=\(\frac{1.2.3+1.2.3.2.2.2+1.2.3.4.4.4+1.2.3.7.7.7}{1.3.5+1.3.5.2.2.2+1.3.5.4.4.4+1.3.5.7.7.7}\)
=\(\frac{1.2.3.\left(1+2^3+4^3+7^3\right)}{1.3.5.\left(1+2^3+4^3+7^3\right)}\)
=\(\frac{1.2.3}{1.3.5}\)
=\(\frac{2}{5}\)