olymmath

HMMT November 2011 U28

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Determine the value of

∑k=12011k−1k!(2011−k)!.\sum_{k=1}^{2011} \frac{k-1}{k!(2011-k)!} .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2009\left(2^{2010}\right)+1}{2011!}

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