Series convergence or divergence . $\sum_{n=1}^\infty \left(\frac{n^4}{n^5+7}\right)$ $$\sum_{n=1}^\infty \left(\frac{n^4}{n^5+7}\right)$$
I try this series by the comparison test with $a_n\le b_n,$ $a_n=\frac{n^4}{n^5+7}$  and $b_n=\frac{n^4}{n^5}=\frac{1}{n}$
then $b_n$ diverges, dose the series diverges ?

Hint:
$$\frac{n^4}{n^5+7}\geq\frac{n^4}{8n^5}=\frac{1}{8n}$$
for all $n\geq1$.
