Hello, this is my first post on MHF.

I was wondering if someone might be able to provide a general set of machinery and tools to evaluate various series (supposing they converge) into their closed form. I know this might not be able to be done for every infinite series.

Sum of the tools I know of are:

Geometric series in the finite and the infinite sum case

Expression for (1-x)^(-k)

sines, cosines, exp

For example, if I wanted to evaluate a series such as: (sum from n=1 to infinity) of 1/((3*n-1)*(3*n-2)). I can very well put this into Wolfram and get the desired answer but for my personal use, how would one evaluate such a series?

Thank you for your help.