It is now that we have completed a detailed look at one of the Gospels that we give a better answer to what the Gospels are meant to be about. We know that Luke writes so that his readers will know the certainty of the truth that they have heard and John writes so that his might believe who Jesus is.
What we may add to that is this. First, there is a purpose beyond this. It is not for mere private, personal benefit that we are to know and believe. Rather, all of the Gospel writers have a purpose beyond that. Luke tells us that Jesus had said that his followers were to receive power and to be his witnesses. Matthew describes Jesus commissioning his disciples to do just that. We are meant to be witnesses, sent out as the apostles were sent in order to make more disciples.
How do the Gospel writers help us to believe so that we are equipped to witness. Well, the clues are there in Luke 24. They do so by not just reporting on the life of Jesus but showing how his life, death and resurrection, his every word and action is a fulfilment of the whole of Scripture. Jesus is the one who fulfils the law and the prophets so that we can receive forgiveness through repentance.