<s>[INST] 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 ?
 [/INST] A bit more formally:
Let $n \ge 2:$
$a_n=\dfrac{n^4}{n^5+7} \gt \dfrac{n^4}{n^5+n^5} =\dfrac{1}{2n}.$
Since $(1/2) \sum \dfrac{1}{n}$  diverges, 
$\sum \dfrac{n^4}{n^5+7}$ diverges (comparison test).
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