Does series 1/e^n conditionally converge?

Question

Does series 1/e^n conditionally converge?

Answer 1

Use the ratio test:

L = lim|a_n+1/a_n|

n→∞

1/eⁿ⁺¹/1/eⁿ = 1/eⁿ

lim |1/eⁿ| = 0

n→∞

L = 0 < 1 So absolute Convergence

If L = 1 then it would be Conditionally Convergent, which it is not.