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# Evaluating an Infinite Sum of a Finite Product

NUMTH-RWEZUW

What is $\sum_{n = 1}^{\infty} \prod_{m = 1}^{n} e^{-2m/(n + 1)}$?

A

$\infty$

B

$\cfrac{1}{e^{1/2} - 1}$

C

$\cfrac{1}{e - 1}$

D

$0$