Question

Let $S=\frac{4}{19}+\frac{44}{{19}^2}+\frac{444}{{19}^3}+\dots upto\infty$. Then $S$ is equal to

• A. 40/9
• B. 38/81
• C. 36/171
• D. none of these

Answer 1

Answer: (B)

38/81

$S=\frac{4}{19}+\frac{44}{{19}^2}+\frac{444}{{19}^3}+\dots$ (1)

$\Rightarrow \frac{1}{19}S=\frac{4}{{19}^2}+\frac{44}{{19}^3}+\dots$ (2)

Subtracting (2) from (1), we get,

$\frac{18}{19}S=\frac{4}{19}+\frac{40}{{19}^2}+\frac{400}{{19}^3}+\dots$

$=\frac{\frac{4}{19}}{1-\frac{10}{19}}$

$=4/9$

$\Rightarrow S=38/81$