$f\left( x \right)=\frac{ 6 }{ \sqrt{ {x}^{5} } }$
Since the function $f\left( x \right)=\frac{ 6 }{ \sqrt{ {x}^{5} } }$ is positive, continuous, and decreasing for $x \geq 1$, use the Integral Test$\int_{ 1 }^{ +\infty } \frac{ 6 }{ \sqrt{ {x}^{5} } } \mathrm{d} x$
To evaluate the improper integral, by definition, rewrite it using a limit and a definite integral$\lim_{a \rightarrow +\infty} \left(\int_{ 1 }^{ a } \frac{ 6 }{ \sqrt{ {x}^{5} } } \mathrm{d} x\right)$
Evaluate the definite integral$\lim_{a \rightarrow +\infty} \left(-\frac{ 4 }{ \sqrt{ a } \times |a| }+4\right)$
Evaluate the limit$4$
Since the limit is finite, the improper integral converges$\textnormal{Convergent}$
Since the integral converges, the given series also converges$\textnormal{Converges}$