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Question Number 34675 by math khazana by abdo last updated on 09/May/18

provethat e = Σ_(k=0) ^n  (1/(k!))  +∫_0 ^1   (((1−t)^n )/(n!)) e^t  dt .

$${provethat}\:{e}\:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{{k}!}\:\:+\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{\left(\mathrm{1}−{t}\right)^{{n}} }{{n}!}\:{e}^{{t}} \:{dt}\:. \\ $$

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