## Calculus (3rd Edition)

Given $$\sum_{n=2}^{\infty} \frac{n^3}{\sqrt{n^7+2n^2+1}}$$ Compare with the divergent series $\displaystyle \sum_{n=2}^{\infty}\frac{1}{n^{1/2}}$ ($p-$series , p<1) and by using the Limit Comparison Test, we get: \begin{align*} \lim_{n\to \infty} \frac{a_n}{b_n}&=\lim_{n\to \infty} \frac{n^{7/2}}{\sqrt{n^7+2n^2+1}}\\ &=1 \end{align*} Then $\displaystyle \sum_{n=2}^{\infty} \frac{n^3}{\sqrt{n^7+2n^2+1}}$ also diverges