Does the comparison test work for this series inequality?

[Square1]

Hey check out the attached picture. I think I solved the issue now but just to confirm perhaps...

If I were to continue here using the comparison test, is the only problem that b-subn limit equals 0, so the comparison test is inconclusive?

Otherwise, since our summation does not included n=0 (or other undefined values right?), my simplified form of a-subn holds, and my inequality is correct?

Thanks for any help.

 

[mathman]

Your picture is hard to read. However, it seems you have a series where for large n, the terms are approximately 1/n, so the series diverges.