Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 13"

Revision as of 09:37, 4 April 2012

$13.$ 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 $1000$ .

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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 {{solution}}
-==See also==
+==See Also==
+{{Mock AIME box|year=Pre 2005|n=3|num-b=12|num-a=14}}

Mock AIME 3 Pre 2005 (Problems, Source)
Preceded by Problem 12	Followed by Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15