Rat's Tail Turning Black

Hello,
about a week ago I noticed the tip (about an inch) of my rat's tail was turning black, and higher up it was still grayish. Today I was picking at it and big flakes of skin were coming off. Underneath it was even more black and smelled a bit. I was pinching his tail as well and he didn't seem to notice, so I think he has lost feeling in it completely. He does not groom the tip of his tail nor does he have a companion, so it couldn't have been damaged by biting. He is an about-two-year-old fancy rat if that info. would be relevant. Can anyone tell me what this might be and possible treatments and causes? I have posted a few pictures as well.
Thanks!


Pictures:

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His tail might have gotten caught and pinched somewhere in the cage. It turns black when it's dying off. It will fall off on it's own eventually. Good that he doesn't notice it. The only thing I would be worried about if it's an infection and it continues up the tail. I would get a sharpie and mark where you see it's grey and keep an eye on it if it goes past your mark then you know it's getting worse and will need to see a vet.

Thanks for your reply Joanne! I will make sure to take your advice!

How is your rat's tail doing?