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will the following converge if they then what are their sums

$\sum_{n=1}^\infty\left[\frac{\left(1+\frac{1}{n}\right)}{e}\right]^n$

$\sum_{n=1}^\infty\left[\frac{\left(1+{1}/{n}\right)^{n+1/2}}{e^n}\right]$

do the above series have any physical meaning (apart from fun).

2 Answers 2