what is the easiest test to determine if this converge conditionally or absolutely?

Question

inf
E (-1)^(n-1) * e^(1/n) / (3n)
n=1

Answer 1

You can use the Alternating Series Test to establish that the series converges.

You can use the Comparison Test (with the divergent series Σ(1/(3n)) to show that the series Σe^(1/n) / (3n) diverges.

Hence, the given series converges conditionally, but not absolutely.