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?
The series should be converging to 0.
As n increases, the numerator will either be -1 or 1. So, let's see what happens to the denominator. As n increases, n^(1/3) will also increase. So, the denominator will increase as n increases. At n = infinity, 1/infinity tends to 0, and so does -1/infinity.