12 HL The Ratio Test

Complete the following questions before our next class.

Use the ratio test to determine the convergence or divergence of the following series.

1. \[\sum_{n=1}^\infty \frac{n^3 3^{n+1}}{4^n}\]
2. \[\sum_{n=1}^\infty \frac{n^{10}}{10^n}\]
3. \[\sum_{n=1}^\infty \frac{n^n}{n!}\]

From the Haese book, complete Exercise K.3 question 1.