My snake was playing in the bathtub and the last half inch of his tail came off. He has always had an injury there so I've always been careful with it, but lately it looked very loose. I didn't even see it come off or where it went but when I was bringing him back to his cage I noticed it missing. Is he going to be OK? Has this happened to anybody before?

He seems fine right now, but I'm not sure if he is, I'm not very experienced with garter snakes. Any advice would be great, should I take him to the vet? It's only a very small piece of tail and it was already hanging off but I'm worried about him.