In reality we have no way to know if our Ramadan was accepted, however there are some signs that our Ramadan was accepted. 

In the Quran 19:76, Allah says: “Allah gives an increase in guidance to those who are guided.” Some scholars say that this contains the secret as to whether your good deeds have been accepted or not. If you conclude your deeds and then you are given an ability to continue and do another good deed after that, that is a sign that your good deeds have been accepted. 

If after Ramadan you are still praying the night prayers, still praying 5 daily prayers and still reading Quran, then this is an indication that your Ramadan has been accepted.