William Burkitt on John 20:30

Observe here, 1. The true end for which the miracles of Christ were so carefully recorded; namely, that we might believe. By believing that Christ is the Son of God, we have life; and by the evidence of his miracles, we know and believe him to have been the Son of God. The miracles which Christ wrought, were the best external evidence of his mission.

Observe, 2. That all Christ's miracles, both before his passion and after his resurrection, were not recorded by the evangelists.

Observe, 3. The great point concerning Christ to be known and believed from the scriptures, is this, that Jesus, the Son of the virgin, is the promised Messiah, the anointed of the Father, he is whom all the types and shadows of the law are accomplished; and that this Jesus is for nature co-essential, for dignity co-equal, and for duration co-eternal with the Father; one in essence, equal in power and glory.

Thus believing that Jesus is the Son of God, and accompanying that belief with a holy life, if we believe well, and live well, we shall have life through his name.