Dic/ some usages/ come to do something

─(7). If someone comes to do something, they do it at the end of a long process or period of time.

• She said it so many times that she came to believe it.

─(8). You can ask how something came to happen when you want to know what caused it to happen or made it possible.

• How did you come to meet him?

─(26). You use the expression come to think of it to indicate that you have suddenly realized something, often something obvious.

• You know, when you come to think of it, this is very odd.

CF.
─(2). When someone comes to do something, they move to the place where someone else is in order to do it, and they do it.
 . In British English, someone can also come and do something and
 . in American English, someone can come do something.
 . However, you always say that someone came and did something.

• Eleanor had come to visit her.
• Come and meet Roger.
• I want you to come visit me.

..... COBUILD

CF. come to do sth: to start to do something:

• I've come to like her over the months.
• It used to hold paper bags, but gradually came to be used for magazines.
• How did that phrase come to mean (=develop so that it means) that?

..... CALD