Decide if sequence converges/diverges

The given sequence is: .

I rearranged terms to get . I couldn't tell by inspection if this is convergent or divergent, so I started plugging in large values of n and noticed that it seems to be that . So now I'm trying to prove it converges by showing that has an upper bound and is non-decreasing. However I'm having trouble showing it has an upper bound, therefore leading me to think maybe that is divergent? I'm not sure at this point, any suggestions would be appreciated.

Thanks in advance.