Infinite Limit?

Calculus Level 3

\[ \large \lim_{n\to\infty} \left( \frac1{e^{\frac12}} + \frac1{e^{\frac23}} + \frac1{e^{\frac34}} + \ldots + \frac1{e^{\frac{n-1}n}} \right ) = \ ? \]

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