Does the infinite series Sigma (n = 1 to infinity) (-1)^n ln( (3n+1)/(3n-3) converge?

Answer 1

(3n+1)/(3n-3) approaches 1 as n approaches infinity

so ln((3n+1)/(3n-3)) approaches ln1 = 0

and

0 times (-1)^n = 0,

it converges to 0,

although initially you might think it doesn't due to the oscillation of (-1)^n back and forth never converging, as it goes from 1 to -1