persvadi

The pair to learn is persvadi against konvinki, and the distinction is worth the effort because English blurs it. Konvinki works on belief: you convince someone that something is true, and their mind changes. Persvadi works on action: you talk someone into doing a thing, and their behaviour changes. You can persuade a person to come to the meeting without convincing them of anything at all, which is most of what politics consists of.

Both take a person as the object. Persvadi then takes an infinitive for the deed: mi persvadis lin resti, I talked him into staying. Konvinki takes ke and a clause for the belief: mi konvinkis lin ke li pravas. Getting the frames right is more of the battle than getting the meanings right.

And the seam. Per is a real preposition, svadi is not a word, so persvadi is not per plus anything. The Latin per is genuinely in the ancestry, just as it is in percepti, and in both cases it stopped being a separable piece the moment Esperanto borrowed the whole verb. If you want the Esperanto prefix per- you will not find it here.