Determine whether the following series converges or diverges. If it converges, determine what it converges to (Verify your answer)

(sqrt(2)/e^2)+(sqrt(2)/e^4)+(sqrt(2)/e^6)+(sqrt(2)/e^8)+...

 

Not sure if I started it out correctly, but I turned it into a geometric series:

infinity ∑ n=1 (sqrt(2)/e^2)^n

 

a=1 & r = (sqrt(2)/e^2)

 

& if I'm right if |r| < 1, then it's convergent. If |r| ≥ 1.