As far as I can tell, if you want to say something like "Would you...?" or "Why don't you..?", it's common to say something like "食べるのだろうか？". I looked it up and as I far as I can tell it's short ...
What does 気負わずに奮ってご参加ください mean? Is it like 気軽にご参加ください? Context: an event information page announcing pre-requisites for attendance: 前提知識 ...