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Summation and Factorials

Algebra Level 3

$\sum_{k=3}^{2000} \frac{k}{(k-2)! + (k-1)! + k!}$

Which of the following choices is the best approximation for the summation above?

\frac12

\frac1{60}

\frac1{12}

\frac16

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by Prakkash Manohar

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