I caught my bf on fb trying to hook up with the same girl,i let him blocked her but he added her again?

My bf is in the army stationed in South Korea,we had issues on facebook about girls hitting on him.I once caught him lying to me about this girl which he says is just a friend but when i got his pword i saw the convo that he was telling the girl i am just a friend too but we were on like 3 months already.we got that settled.One of his so called bestie,which is a girl asked if we are officially in a relationship,he said he is just playing aroud and he denied that i am his gf.that hurts me.I forgave him again.There's this girl who had a kid and lives in New york,which he met on FB too,the girl messaged me that my bf promised to meet up with her and take care of her and will treat her kid as his.we had a big fight,i blocked the girl off his page.After a span of 2 months,i thought we was over it.Now,just today i was looking at his page,cos he wont give me his pword,which i didn't fuss on getting it again.I noticed that it was that girl from NewYork,she used a different name and she only got 4 friends on her page which is my BF,her original fb page and 2 other females.I confronted my bf he acts like he wasnt aware and try to play safe.Funny thing was,after i confronted him the girl blocked me from seeing that page.I was thinking they were chatting at the same time.So i throw in the towel for the 5th time.He begged and cried to win me back but i think im totally done this time.He still believes that i will take him back but i know im not getting back with him.What should i do to be totally over him?i know he would bug me on fb and try calling me like crazy begging me back.HELP!