Answer
Convergent.
Work Step by Step
$\int_{1}^{\infty} (x^{-3})dx=\lim\limits_{t \to \infty}\int_{1}^{t} (x^{-3})dx=\lim\limits_{t \to \infty}[-\frac{1}{2}x^{-2}]_{1}^{t}=0--\frac{1}{2}=\frac{1}{2}$
Hence, the given series is convergent by the Integral Test.
