__Question:__

If the following series converges, compute its sum. Otherwise, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, and DIV otherwise.

I know that I can get 1(2n+4) - 1/2n as the partial fraction decomposition within the sum and that I need to write the terms to see the pattern and all that so that's not my problem. My problem is that I'm having trouble seeing the pattern and would appreciate it if someone could show me their work and explain their logic.

Any help would GREATLY appreciated!

Thanks in advance!