# Chapter 11 - Infinite Series - 11.3 Convergence of Series with Positive Terms - Exercises - Page 556: 20

Converges

#### Work Step by Step

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.

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