Question

Find the value of $\cdot 1\dot{2}\dot{3}$ regarding it as a geometric series

• A. $\frac{66}{499}$
• B. $\frac{66}{495}$
• C. $\frac{61}{495}$
• D. $\frac{60}{499}$

Answer 1

Answer: (C)

$\frac{61}{495}$

$Letx=0\cdot 1\dot{2}\dot{3}$

$10x=\mathrm{1.23232323232323......}$

$1000x=\mathrm{123.232323.....}$

Subtracting Both we get

$990x=122$

$x=\frac{61}{495}$