MathDB
Limiting Sum of an Infinite Series

Source:

March 3, 2010

Problem Statement

The limiting sum of the infinite series, \frac{1}{10} \plus{} \frac{2}{10^2} \plus{} \frac{3}{10^3} \plus{} \dots whose n nth term is n10n \frac{n}{10^n} is: <spanclass=latexbold>(A)</span> 19<spanclass=latexbold>(B)</span> 1081<spanclass=latexbold>(C)</span> 18<spanclass=latexbold>(D)</span> 1772<spanclass=latexbold>(E)</span> larger than any finite quantity <span class='latex-bold'>(A)</span>\ \frac19 \qquad <span class='latex-bold'>(B)</span>\ \frac{10}{81} \qquad <span class='latex-bold'>(C)</span>\ \frac18 \qquad <span class='latex-bold'>(D)</span>\ \frac{17}{72} \qquad <span class='latex-bold'>(E)</span>\ \text{larger than any finite quantity}