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Question Number 151026 by qaz last updated on 17/Aug/21

Σ_(n=0) ^∞ (0^n /(n!))=?

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{0}^{\mathrm{n}} }{\mathrm{n}!}=? \\ $$

Answered by ArielVyny last updated on 17/Aug/21

according to the  definition   e^t =Σ_(n=0) ^∞ (t^n /(n!)) then Σ_(n=0) ^∞ (0^n /(n!))=e^0 =1

$${according}\:{to}\:{the}\:\:{definition}\: \\ $$$${e}^{{t}} =\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{t}^{{n}} }{{n}!}\:{then}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{0}^{{n}} }{{n}!}={e}^{\mathrm{0}} =\mathrm{1} \\ $$

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