Question

Let $S =2+\frac{6}{7}+\frac{12}{7^{2}}+\frac{20}{7^{3}}+\frac{30}{7^{4}}+\ldots . .$ then $4 S$ 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)

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