Ratio and Root Tests Quiz

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  1. Does $\sum_{n=1}^\infty \dfrac{(n+2)!}{10^n \cdot n!}$ converge?


  2. Does $\sum_{n=1}^\infty \dfrac{n^n}{3^n}$ converge or diverge?


  3. Test $\sum_{n=1}^\infty ne^{-n}$ for convergence.


  4. Test $\sum_{n=1}^\infty \dfrac{2^n}{3^n \cdot 4n}$ for convergence.


  5. Test $\sum_{n=1}^\infty \dfrac{(-1)^{n-1} n!}{n^n}$ for convergence.



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