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

Question

Quizplus · Accepted Answer

This is a geometric series with the first term $a = 0.1$ and common ratio $r = 0.1$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting the given values, we get $S = \frac{0.1}{1 - 0.1} = \frac{0.1}{0.9} = \frac{1}{9}$.

Find the Sum, If It Exists 0.1+0.01+0.001+0.0001+…0.1 + 0.01 + 0.001 + 0.0001 + \ldots0.1+0.01+0.001+0.0001+…

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