убежда́ться

verbreflexiveimperfective (partner убеди́ться)rare

1.
to become convinced, to make sure, to satisfy oneself, to see for oneself
Я всё бо́льше убежда́юсь, что он прав.
I'm becoming more and more convinced that he is right.
Usually with в + prepositional case or with a что-clause; imperfective of убедиться.
2.
(rare) to come to realize, to become aware
Он ма́ло-пома́лу убежда́лся в со́бственном бесси́лии.
Little by little he became aware of his own helplessness.
Bookish; of an insight that dawns on someone over time.

Examples

В кото́рый раз я убежда́юсь, что ты и́стинный фило́соф.
For the umpteenth time, I see that you are a true philosopher.
Я вновь убежда́юсь, что ты и́стинный фило́соф.
Once again, I see that you are a true philosopher.
Я каждый раз убеждаюсь, что он прав.
Every time, I become convinced that he is right.

Imperative
ты	убежда́йся
вы	убежда́йтесь

Active present	убежда́ющийся	convincing oneself, becoming convinced
Active past	убежда́вшийся	persuading oneself, convincing oneself, in the process of being convinced
Passive present	-
Passive past	-
Gerund present	убежда́ясь	while doing (present)
Gerund past	убеждавшись	while doing (past)