Consider the series ∑n=1to ∞ (−3/ arctan(n) )^n. Evaluate the the following limit. lim n→∞ ( |a(n) |) ^(1/n)

Question

Consider the series ∑n=1to ∞ (−3/ arctan(n) )^n.

Evaluate the the following limit. lim n→∞ ( |a(n) |) ^(1/n)

Answer 1

Looks like your posting a lot of questions at once, so I'll give you a hint. First, what is the nth root of (-3/ arctan(n))^n? Once you find that, it may be helpful to know lim n →∞ arctan(n), think about the graph of arctan(x). Now use the root test and see what you get!