Answer
Converges Absolutely
Work Step by Step
Consider $a_n=\dfrac{1}{\sqrt {n(n+1)(n+2)}}$
Since, we see that
$\Sigma_{n=1}^\infty \dfrac{1}{\sqrt {n(n+1)(n+2)}} \lt \Sigma_{n=1}^\infty \dfrac{1}{\sqrt {(n)(n)(n)}}=\Sigma_{n=1}^\infty \dfrac{1}{{\sqrt [3] {n}}}$
Now, $\Sigma_{n=1}^\infty \dfrac{1}{{\sqrt [3] {n}}}=\Sigma_{n=1}^\infty \dfrac{1}{n^{3/2}}$
Thus, the series $\Sigma_{n=1}^\infty \dfrac{1}{n^{3/2}}$ is a convergent p-series.
Hence, the given series Converges Absolutely by the direct comparison test.
