/sci/ - Science & Math

I have 2 questions about the comprehension of this.

1) This is on the 2nd bullet point: if (c) is between 0 and infinity, then both a_n and b_n converges, and if (c) is less than 0, both a_n and b_n diverges right?

2) Does it matter what I choose for b_n? for example, if the original function a_n = (lny)/(y^3), then does b_n need to be something SIMILAR to a_n? my prof told me that it can be 'anything' which was extremely confusing for me.