Homework 13 problem 2

I am having some trouble with problem 2 on the homework, this is what I have come up with, but I can’t figure out which is wrong. I think
#1) Diverges with Comparision Test
#2) Converges but uses the Geometric Test
#3) Converges with Comparision Test
#4) Diverges with the Limit Comparision Test
#5) Converges but not with the Limit Comparision or Comparision Tests

Any advice/help is appreciated.

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I think #2 is the one you got wrong; the others all look fine to me.

Sorry it took me a while to get to this. Feel free to email me, if I haven’t at least acknowledged a question within a day or so!