Acts 18

I think a great lesson is taught as Paul -

"...reasoned in the synagogue every sabbath, and persuaded the Jews and the Greeks.
5 And when Silas and Timotheus were come from Macedonia, Paul was pressed in the spirit, and testified to the Jews that Jesus was Christ."  (New Testament | Acts 18:4 - 5)

I seems apparent to me that Paul did everything he though possible in teaching these Jews and Greeks.  And finally -

"...when they opposed themselves, and blasphemed, he shook his raiment, and said unto them, Your blood be upon your own heads; I am clean: from henceforth I will go unto the Gentiles."  (New Testament | Acts 18:6)

Obviously, Paul thought the Jews were to steep in tradition and stubborn and basically moved on.  Then Luke writes the rest of the story as  Paul -

"...departed thence, and entered into a certain man's house, named Justus, one that worshipped God, whose house joined hard to the synagogue."  (New Testament | Acts 18:7)

And while what appears living next door -

"...Crispus, the chief ruler of the synagogue, believed on the Lord with all his house; and many of the Corinthians hearing believed, and were baptized.
9 Then spake the Lord to Paul in the night by a vision, Be not afraid, but speak, and hold not thy peace:
10 For I am with thee, and no man shall set on thee to hurt thee: for I have much people in this city.
11 And he continued there a year and six months, teaching the word of God among them."  (New Testament | Acts 18:8 - 11)

You just never know who will eventually repent and be converted.  The Savior taught in the Americas -

"...for unto such shall ye continue to minister; for ye know not but what they will return and repent, and come unto me with full purpose of heart, and I shall heal them; and ye shall be the means of bringing salvation unto them."  (Book of Mormon | 3 Nephi 18:32)