## Calculus (3rd Edition)

Given $$\sum_{n=1}^{\infty} \frac{n^3}{n^5 + 4n+1}$$ We compare the given series with the series $\displaystyle\sum_{n=1}^{\infty} \frac{1}{n^2 }$, which is a convergent series ( $p-$ series with $p=2$) and for $n>1$ $$\frac{1}{n2^n}\leq\frac{1}{2^n}$$ Then $\displaystyle\sum_{n=1}^{\infty} \frac{n^3}{n^5 + 4n+1}$ also converges.