I would definitely not email him. Chasing and begging never works. Trust me. I tried it and all it does is just push that person farther away from you. It saids that you haven't talked to him in months, expect for that letter, which I am assuming you poured your heart to him? Big mistake because now he has the control over the situation. He knows that whatever happens out there, if he doesn't see anyone he likes or finally had his fun, he could always come back to you.
You want to be the one in control. I don't know if you heard about "no contact"?
link Above is the link that describes it very in detail. I would try this first to see how it goes. Go out. Have fun with your friends and don't get caught up on what he is doing, it's summer. Maybe you won't see him everyday of the summer but I'm sure you guys might bump into each other. Don't be rude just casual conversation. Hey, what's up and that's about it. Keep it short and always be the person to end it. Once he starts realizing that you are not a spare tire, one who he could always come back at any time, he'll start to think about the decision.
Whatever you do try not to talk about you guys in the past, it will only hurt all the work you put in before. Try that, see how it works. Hope it helps. Remember it's summer, go out there and just enjoy it.