Question

Let $S=2+\frac{6}{7}+\frac{12}{7^2}+\frac{20}{7^3}+\frac{30}{7^4}+\dots ..$ then $4S$ is equal to

• A. ${\left(\frac{7}{3}\right)}^2$
• B. $\frac{7^3}{3^2}$
• C. ${\left(\frac{7}{3}\right)}^3$
• D. $\frac{7^2}{3^3}$

Answer 1

Answer: (C)

$\Rightarrow \frac{6^{2}S}{7^2}=\frac{2}{1-\frac{1}{7}}=\frac{2}{6}\times 7$
$\Rightarrow S-\frac{2\times 7^3}{6^3}\Rightarrow 4S-\frac{7^3}{3^3}-{\left(\frac{7}{3}\right)}^3$