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

 
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==Problem==
 
<math>13.</math> Let <math>S</math> denote the value of the sum
 
<math>13.</math> Let <math>S</math> denote the value of the sum
  
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Determine the remainder obtained when <math>S</math> is divided by <math>1000</math>.
 
Determine the remainder obtained when <math>S</math> is divided by <math>1000</math>.
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==Solution==
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{solution}

Revision as of 06:53, 2 April 2007

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 $1000$.

Solution

{solution}