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Well, I know the mathematical description of e as $\lim_{n\to\infty}(1-\frac{m}{n})^{n}=e^{-m}$ ,but today in my statistical mechanics class, while calculating the volume of thin shell of thickness 's' of n-dimensional hypersphere of radius R, he used this expression $(1-\frac{s}{R})^n=e^{-\frac{sn}{R}}$ I haven't been able to figure it out on how did it come from, since it doesn't match with the definition of $e^{-m}$

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  • $\begingroup$ Still, couldnot figure it out $\endgroup$ – Roshan Shrestha Nov 20 '14 at 16:15
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$\lim\left(1-\frac{s}{R}\right)^n = \lim\left(\left(1-\frac{s}{R}\right)^R\right)^{\frac{n}{R}} = \left(e^{-s}\right)^{\frac{n}{R}} = e^{-\frac{sn}{R}}$

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  • $\begingroup$ Thanks a lot !!! $\endgroup$ – Roshan Shrestha Nov 20 '14 at 16:16

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