Colossians 1:10

To walk worthily of the Lord

(περιπατησα αξιως του Κυριου). This aorist active infinitive may express purpose or result. Certainly this result is the aim of the right knowledge of God. "The end of all knowledge is conduct" (Lightfoot). See 1 Thessalonians 2:12; Philippians 1:27; Ephesians 4:1 for a like use of αξιως (adverb) with the genitive.In the knowledge of God

(τη επιγνωσε του θεου). Instrumental case, "by means of the full knowledge of God." This is the way for fruit-bearing and growth to come. Note both participles (καρποφορουντες κα αυξανομενο) together as in verse Colossians 1:6.Unto all pleasing

(εις πασαν αρεσκιαν). In order to please God in all things (1 Thessalonians 4:1). Αρεσκια is late word from αρεσκευω, to be complaisant (Polybius, Plutarch) and usually in bad sense (obsequiousness). Only here in N.T., but in good sense. It occurs in the good sense in the papyri and inscriptions.