Answer
$\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges.
Work Step by Step
If $\Sigma^{\infty}_{ n=1} a_{n}$ converges, then by divergence test : $\lim\limits_{n \to \infty}a_{n}=0$
Which in turn implies that $\lim\limits_{n \to \infty} \frac{1}{a_{n}} \ne 0$
As per the divergence test we can conclude that $\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges.
Hence, $\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges.
