# Math Help - convegent or divergent by Alternating Series Test

1. ## convegent or divergent by Alternating Series Test

Please help to determine whether the series is convergent or divergent by Alternating Series Test.
(-1)^n (2n-1)/2n
My reasoning a(n+1) = (2n+1)/(2n+2)
a(n+1) less or equal to an. This is where I am having a problem. It looks like it is wrong. Right?
Then what? The test failed?
Thank you

2. Alternating test does not apply because one of the conditions required to use it fails, namely: $\lim_{n \to \infty} \frac{2n-1}{2n} \neq 0$