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Mock AIME 3 Pre 2005 Problems/Problem 13

Revision as of 22:05, 24 February 2007 by Me@home (talk | contribs)
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$13.$ 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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