Find the sum
\[0.1 + 0.02 + 0.003 + 0.0004 + \dots + \frac{n}{10^n} + \dotsb.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the sum
\[0.1 + 0.02 + 0.003 + 0.0004 + \dots + \frac{n}{10^n} + \dotsb.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{10}{81}
Find the sum
\[0.1 + 0.02 + 0.003 + 0.0004 + \dots + \frac{n}{10^n} + \dotsb.\]
train