# Thread: sum of series

1. ## sum of series

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?

2. Originally Posted by godai
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?
Since the answer given to you by Mathematica is wrong, you must have incorrectly typed the input.

By the way, why did you ask "What is the sum" ....? Determining whether or not the series converges is NOT the same thing as finding the sum of the series.

3. oops what I meant was does the series converge or not? ><

4. 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.

5. i think you mean the general term, finding its sum could be hard!