## Calculus (3rd Edition)

Given $$\sum_{k=2}^{\infty}\frac{ k^{1/3} }{k^{5/4}-k}$$ Compare with $\displaystyle\sum_{k=1}^{\infty}\frac{1}{k^{11/12}}$, which is a divergent series ( $p-$series with $p<1$) and for $k\geq 2$ \begin{align*} \frac{ k^{1/3} }{k^{5/4}-k} &\geq \frac{1 }{k^{11/12}} \end{align*} Then $\displaystyle\sum_{k=2}^{\infty}\frac{ k^{1/3} }{k^{5/4}-k}$ also diverges.