I assume you want to know if they converge or not. For number 2, you would use the comparison test (compare to ).

Number 1 is pretty tricky. I'm pretty sure it diverges - as n goes to infinity, looks like and looks like 1, so your series looks like a harmonic series. But that's not a proof - that's just intuition.

If you use and , then I think you can prove divergence. The series you compare against will be the harmonic series with some convergent series added or subtracted. They don't affect the divergence.

You might have heard of the limit comparison test - you should check if this applies.

Let us know how it goes.

- Hollywood