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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?

\[\frac1{60}\] \[\frac1{12}\] \[\frac16\] \[\frac12\]

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by Prakkash Manohar

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