I have Pokemon White and I don't have anyone to trade with and since the servers are gone, How will i be able to finish the pokedex?
Your first stumbling block will be event Pokemon.
Simply put, without someone to trade with, you wont. You can still trade locally, but if you have no-one to trade with nearby you won't be able to get certain Pokemon.
That said, if you simply discount event Pokemon, then it is possible to get the rest of the national dex, but you'll need to at least purchase Pokemon Black, as well as Heartgold/Soul Silver, Diamond/Pearl/Platinum, and possibly the R/S/E games as well.