20 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.”
21 ἀρεσκεία states that ἀρεσκείαν (areskeian) refers to a “desire to please εἰς πᾶσαν ἀ. to please (the Lord) in all respects Col 1:10.”

In other versions

ESVEnglish Standard Version

so as to walk in a manner worthy of the Lord, fully pleasing to him: bearing fruit in every good work and increasing in the knowledge of God;

NIVNew International Version (2011)

so that you may live a life worthy of the Lord and please him in every way: bearing fruit in every good work, growing in the knowledge of God,

CSBChristian Standard Bible

so that you may walk worthy of the Lord, fully pleasing to him: bearing fruit in every good work and growing in the knowledge of God,

NLTNew Living Translation

Then the way you live will always honor and please the Lord, and your lives will produce every kind of good fruit. All the while, you will grow as you learn to know God better and better.

LEBThe Lexham English Bible

so that you may live in a manner worthy of the Lord, to please him in all respects, bearing fruit in every good deed and increasing in the knowledge of God,

KJV 1900King James Version

That ye might walk worthy of the Lord unto all pleasing, being fruitful in every good work, and increasing in the knowledge of God;

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