Finitely :: Finitely (adv.) In a finite manner or degree.
Indefinitely :: Indefinitely (adv.) In an indefinite manner or degree; without any settled limitation; vaguely; not with certainty or exactness; as, to use a word indefinitely..
Infinitely :: Infinitely (adv.) Without bounds or limits; beyond or below assignable limits; as, an infinitely large or infinitely small quantity..