Ok
That makes it 2 liters? In my opinion thats too small for a Betta but we can work with it until you get a bigger tank.
Till then.
You will need to do daily water changes of 50 to 75 % with dechlorinated water, This is a must.
What type of water conditioner do you have?
How cold dose it get at your place right now? Bettas need a heater so unless your place is in around 26 deg C ( about 80 F) you need a heater kinda fast.
We can deal with ammonia in the tank with water changes and some floating plants, I would recommend water sprite.
The next issue is water temperature, Can you tell me what country you live in and I will look for a heater for that tank?
What are you feeding him?
How much?
How Often?
Feeding correctly is vital because uneaten food causes ammonia, fish poop causes ammonia, overfeeding fish is bad for the fish.
Look I know you came here asking about his tail and are now getting bombarded with questions and Im sorry but depending on your answers I see some real problems in the next week or less.