Question

The sum of 0.2+0.004+0.00006+0.0000008+....... to $\infty$ is

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is B

$S=\frac{2}{10}+\frac{4}{{10}^3}+\frac{6}{{10}^5}+\frac{8}{{10}^7}+....to\infty$

$=\frac{\frac{2}{10}}{1-\frac{1}{{10}^2}}+\frac{2\times \left(\frac{1}{{10}^2}\right)}{{(1-\frac{1}{10})}^2}$

= $\frac{20}{99}+\frac{200}{9801}$

= $\frac{2000}{9801}$