Simple series question. $\sum_{n=0}^\infty \frac{1}{((n^5)+1)^\frac{1}{3}}$ I think this converges due to direct comparison with $\frac{1}{n^{5/3}}$ but I can't double check this anywhere.

Right.
$(n^5+1)^{1/3}
\gt (n^5)^{1/3}
=n^{5/3}
$
so the sum converges by the $p$-test:
$\sum \dfrac1{n^p}$
converges for
$p > 1$
(easily proved by the
integral test)
and diverges for
$p \le 1$.
