John 20:30-31

Jesus performed many other signs in the presence of his disciples, which are not recorded in this book. But these are written that you may believe that Jesus is the Messiah, the Son of God, and that by believing you may have life in his name.

Jesus performed many other signs in the presence of his disciples 
John 2:11  What Jesus did here in Cana of Galilee was the first of the signs through which he revealed his glory; and his disciples believed in him.
John 2:23  Now while he was in Jerusalem at the Passover Festival, many people saw the signs he was performing and believed in his name.
John 3:2  He came to Jesus at night and said, "Rabbi, we know that you are a teacher who has come from God. For no one could perform the signs you are doing if God were not with him."
John 6:2  ... and a great crowd of people followed him because they saw the signs he had performed by healing the sick.
John 6:26  Jesus answered, "Very truly I tell you, you are looking for me, not because you saw the signs I performed but because you ate the loaves and had your fill."

which are not recorded in this book 
John 21:25  Jesus did many other things as well. If every one of them were written down, I suppose that even the whole world would not have room for the books that would be written.

But these are written that you may believe 
John 3:15-16  "... that everyone who believes may have eternal life in him." For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
John 3:36  Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God's wrath remains on them.

that Jesus is the Messiah, the Son of God 
John 17:1-3  After Jesus said this, he looked toward heaven and prayed: "Father, the hour has come. glorify your Son, that your Son may glorify you. For you have granted him authority over all people that he might give eternal life to all those you have given him. Now this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent." 

Scriptures taken from the Holy Bible, New International Version® NIV®, 
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