David Pawson on Greek verb tenses:
Greek has a “present continuous” tense for verbs which is not easily translated into English but is so often crucial to a proper understanding of the text. It means to be continually doing something. To translate the sense into English, it is necessary to add the two little words “go on.”
For example, Jesus did not say, “Ask and you will receive, seek and you will find, knock and it will be open to you.” implying that each action need only be done once. He actually said, “Go on asking and you will receive, go on seeking and you will find, go on knocking and it will be open to you.” So if someone does not receive the Holy Spirit when they first ask, they should not panic: they should go on asking.
This present continuous verb is used [in John 20:31] so that the verse is more properly translated: “These are written that you may go on believing that Jesus was the Son of God and by going on believing you will go on having life.” The same construction illuminates the best known verse in the Gospel. John 3:16 is better understood as, “For God so loved the world that He gave His only begotten Son, that whoever goes on believing will never perish, but go on having eternal life.”
Jojo Agot 