in order to; for the purpose of ~
A formal, written pattern meaning 'in order to', used with verbs to express purpose.
べく is a formal, written-language pattern that expresses purpose, similar to ために but with a more bookish tone. It is often used in announcements, essays, speeches, or formal reports. In conversation it sounds stiff, so learners should avoid using it in casual speech.
To form it, take the dictionary form of a verb and add べく. For verbs that end in する, use すべく (the old form of する). For example, 勉強する becomes 勉強すべく, not 勉強するべく. Also note that べく is followed by a clause that describes an action taken to achieve the purpose.
Because it is formal, it often appears with verbs like 努力する, 決意する, or action verbs, and the sentence often ends with past tense or a formal verb.