▼ The infinitive περιπατῆσαι (peripatēsai, “to walk, to live, to live one’s life”) is best taken as an infinitive of purpose related to “praying” (προσευχόμενοι, proseuchomenoi) and “asking” (αἰτούμενοι, aitoumenoi) in v. 9 and is thus translated as “that you may live.”

▼ BDAG 129 s.v. ἀρεσκεία states that ἀρεσκείαν (areskeian) refers to a “desire to please εἰς πᾶσαν ἀ. to please (the Lord) in all respects Col 1:10.”