Mock AIME 3 Pre 2005 Problems/Problem 13

Problem

$13.$ Let $S$ denote the value of the sum

$\left(\frac{2}{3}\right)^{2005} \cdot \sum_{k=1}^{2005} \frac{k^2}{2^k} \cdot {2005 \choose k}$

Determine the remainder obtained when $S$ is divided by $1000$ .

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Mock AIME 3 Pre 2005 (Problems, Source)
Preceded by Problem 12	Followed by Problem 14
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