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a. Consider the following limit as a fact:

lim n-> infinity ((n!)^1/n)/n = 1/e

Use this limit to study the convergence of this series using the root test.
Sum of infinity and n=1 of ((3^n)n!)/n^n

b. Use the ratio or the root test to determine the convergence of the series:
Sum of infinity and n=1 of arctan(e^-n), Sum of infinity and k=1 of sqroot(3^k)/(2^k)

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