Find the Sum, If It Exists $$0.1 + 0.01 + 0.001 + 0.0001 + \ldots$$

Multiple Choice

Find the sum, if it exists.
- $$0.1 + 0.01 + 0.001 + 0.0001 + \ldots$$

A) $\frac { 111 } { 1000 }$
B) $\frac { 1 } { 9 }$
C) $\frac { 11 } { 100 }$
D) Does not exist