convergence divergence - Find the partial sum of a given series?

I found this thread, but since it says that I can't ask for help there, I'm making a new one.
How to find the partial sum of a given series?

I have this series (WolframAlpha):
$$\sum_{n = 3}^\infty \frac{1}{n(n - 2)}$$

And I need the partial sum formula. I don't get how it is derived. I got to the partial fraction decomposition described in the linked thread. I made it to the point where I ahd to put the newly found coefficients into the sum. This is what I got:
(WolframAlpha).
Ignore the output. Now how do I get from it to the partial sum formula in the first Wolfram Alpha link?