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1962 AMC 12 Question 40

AMC12 · 1962 AMC 12

Question 40

The limiting sum of the infinite series $$
\frac1{10}+\frac2{10^2}+\frac3{10^3}+\cdots,
$$ whose $n$th term is $\frac{n}{10^n},$ is:
  1. $\dfrac19$
  2. $\dfrac{10}{81}$
  3. $\dfrac18$
  4. $\dfrac{17}{72}$
  5. larger than any finite quantity