1/n^(1+1/n) is convergent or divergent series where n is from 1 to infinity?

Answer 1

Hint:
Write as
(1/n)(1/n^(1/n))
The series 1/n diverges, and what will 1/n^(1/n) go to as n goes to infinity?

Answer 2

(1 + 1/n) ---> 1 as n ---> infinity
So n^(1+ 1/n) ----> n as n -----> infinity
So n^(1 + 1/n) ---> infinity as n ----> infinity
So 1/n^(1 + 1/n) ----> 0 as n -----> infinity