Answer
Convergent by p test.
Work Step by Step
$\Sigma n^{-3}$
$\int_{1}^{\infty} (x^{-3})dx=\lim\limits_{t \to \infty}\int_{1}^{t} (x^{-3})dx=\lim\limits_{t \to \infty}[-\frac{1}{2}x^{-2}]_{1}^{t}=0--\frac{1}{2}=\frac{1}{2}$
Finite value
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