hey guys I'm not sure if this is the right place to post or is it analysis?

anyways, what is the sum of

Sum (-1)^n / (n^(1/3) - 0.5) ? from 1 to infinity

I have tried using the alternating test

the sequence, 1 / (n^(1/3) - 0.5) is decreasing and tends to 0 right?

but I tried on mathematica and it says the series does not converge?