"To convince the reader" means to persuade or influence the reader by presenting strong arguments, evidence, or explanations in order to make them agree with or believe in a certain idea, opinion, or perspective. Full definition
Your resume should quickly and clearly convince the reader of your competence as a manager. (best-job-interview.com)
These types of essays are the most common one because it shows a student's mental ability to analyze and convince the reader about his point based on sturdy research work and references. (trcb.com)
The third alternative — keeping prices high for reasons that don't convince readers — isn't a winning business strategy for selling their products. (madgeniusclub.com)