I can't remember much from my intro. analysis class anymore. If you have an infinite series that ultimately converges, can the first few terms diverge (i.e., can they move away from the convergence point)? And if so, how many of these terms can do so? I'm trying to understand how to "get a feel" for a divergent series. If the first 5000 terms increase, I still can't assume that the rest of the terms will also increase... right?