man, so I asked some people about some questions, and they confuse the heck out of me, so i'm gonna stay here for a while. anyways, all I want to do is to prove ((-1)^n)n/(n+1) converge or diverge. I claim it is divergent, but others claim that (-1)^n doesn't converge nor diverge..... confused. anywys, can you guys check it for me. so for my proof, I multiply top and bottom by 1/n, and I get (-1)^n/(1+ 1/n). taking the limit, I see that the bottom will tend to 1, and the top will just go from -1 to 1. so this becomes *something that diverges*/1. which means this divergres.....is this valid? 2. n^2 /(n+1). again, I multiply by 1/n, and get n/(1+1/n). again, the top will diverge, and the bottom will tend to 1. So is it ok to say that this will diverge because it is *something that diverges*/1? 3. (2n^2 + 3)/(n^2 + 1). same thing, multiply by 1/n, and get (2n + 3/n)/(n + 1/n). ok, so if I get stuck here. Can I take the limit of the 3/n and 1/n, and let them tend to 0. and then this becomes 2n + 0/ n + 0, which simplifies to 2. but I feel bad about this, because I'm not taking the limit of everything at the same time...you know?