Why did Saul go to Damascus after persecuting believers in Jerusalem and Judea?
Saul went to Damascus because he was not satisfied with persecuting believing Jews in Jerusalem and Judea. He intended to go after believing Jews there too, acting in the name of religion and thinking he served God by stamping out faith in Jesus of Nazareth.
Les explains that Saul of Tarsus began his rampage against the believing Jews when Stephen was martyred. These Jerusalem believers were an Ecclesia, a called-out assembly, called out of Judaism but still under Judaism's umbrella and not separated from the Law or temple worship. Saul was not satisfied with what he had accomplished in Jerusalem, Judea, and surrounding areas, so he wanted to go after the believing Jews at Damascus as well. He did all this in the name of religion, thinking he was doing God a service by stamping out any belief in Jesus of Nazareth.