Question

# Determine whether the following series converges or diverges: sum_(n = 1)

Series
Determine whether the following series converges or diverges:
$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{{n}^{{3}}+{n}^{{4}}}}{{n}^{{5}}}.$$

$$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{{n}^{{3}}+{n}^{{4}}}}{{n}^{{5}}}=$$
$$\displaystyle={\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{2}}}+{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}}$$
As $$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{2}}}$$ is convergent by p-series test and $$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}}$$ is divergent,