## Calculus (3rd Edition)

Given $$\sum_{n=1}^{\infty}\frac{n^3}{5^n}$$ By using Ratio Test, we get: \begin{aligned} \rho &=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right| \\ &=\lim _{n \rightarrow \infty} \frac{(n+1)^{3}}{5^{n+1}} \cdot \frac{5^{n}}{n^{3}} \\ &=\lim _{n \rightarrow \infty} \frac{1}{5}\left(1+\frac{1}{n}\right)^{3} \\ &=\frac{1}{5} \end{aligned} Thus the series converges.
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