Answer
Diverges
Work Step by Step
$\lim _{n\rightarrow \infty }\dfrac {1}{4+e^{-n}}=\dfrac {1}{4+0}=\dfrac {1}{4}\neq 0\Rightarrow \sum ^{\infty }_{n=1}\dfrac {1}{4+e^{-n}}$. Diverges
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