Using the root test or otherwise, determine whether the given series
converges or diverges.
∞
A) ∑ (n^2+1/2n^2+n)^n
n=1
∞B) ∑ (1-2/n)^n^2
n=1
I think you mean
(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
n=1
The nth root of that is . What is the limit of that? (You really need to know that .)