I can't read your post. What is in the numerator, what is in the denominator, what is being taken to the n-th power? Use more parentheses.
(what you wrote was a sum of )
Since you mention the root test, the nth root of each term is . What is the limit of that as n goes to infinity? What does that tell you about the sum?
Here, I assume you meann=1
∞B) ∑ (1-2/n)^n^2
The nth root of that is . What is the limit of that? (You really need to know that .)