Question

The sum of the infinite series $\frac{3}{11}+\frac{33}{11^2}+\frac{333}{11^3}+\dots \dots$ is

• A. 3
• B. $\frac{33}{10}$
• C. $\frac{30}{11}$
• D. None of these

Answer 1

Answer: (B)

$S=\frac{3}{11}+\frac{33}{11^2}+\frac{333}{11^3}+\dots \dots$
$\frac{S}{11}=\frac{3}{11^2}+\frac{33}{11^3}+\dots \dots$
$\frac{10}{11}S=\frac{3}{11}+\frac{30}{11^2}+\frac{300}{11^3}+\dots ..$
$\Rightarrow S=\frac{11}{10}\times \frac{\frac{3}{11}}{1-\frac{10}{11}}=\frac{33}{10}$