Question

The value of the expression $\left(\frac{1 \cdot 2 \cdot 4+2 \cdot 4 \cdot 8+\ldots \ldots . .+n \cdot 2 n \cdot 4 n}{1 \cdot 3 \cdot 9+2 \cdot 6 \cdot 18+\ldots \ldots .+n \cdot 3 n \cdot 9 n}\right)^{\frac{1}{3}}$, is

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{9}$
• D. $\frac{8}{27}$

Answer 1

Answer: (B)

$\left(\frac{\displaystyle\sum_{r=1}^n 8 r^3}{\displaystyle\sum_{r=1}^n 27 r^3}\right)^{\frac{1}{3}}=\left(\frac{8}{27}\right)^{1 / 3}=\frac{2}{3}$