Question

C=\(\frac{1.2.3+2.3.4+3.4.5+4.5.6+5.6.7}{3.6.9+6.9.12+9.12.15+12.15.18+15.18.22}\)+\(\frac{8}{27}\)

Answer 1

\(C=\frac{1.2.3+2.3.4+3.4.5+4.5.6+5.6.7}{3.3.2.3.3.1+2.3.3.3.4.3+3.3.4.3.3.5+3.4.5.3.6.3+3.5.3.6.7.3}+\frac{8}{27}\)

\(C=\frac{1.2.3+2.3.4+3.4.5+4.5.6+5.6.7}{3^3.\left(1.2.3+2.3.4+3.4.5+4.5.6+5.6.7\right)}+\frac{8}{27}\)

\(C=\frac{1}{3^3}+\frac{8}{27}=\frac{1}{27}+\frac{8}{27}=\frac{9}{27}=\frac{1}{3}\)

Vậy C = \(\frac{1}{3}\)