Answer
Diverges
Work Step by Step
$\lim _{n\rightarrow \infty }k^{\frac {1}{k}}=\lim _{k\rightarrow \infty }e^{\ln k^{\frac {1}{k}}}=\lim _{k\rightarrow \infty }e^{\frac {\ln k}{k}}=e^{0}=1\neq 0$ then series diverges
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