Note: すべく is the classical form and preferred in formal writing; するべく is also acceptable.
べく is a classical/literary conjunctive form of べし (expressing obligation or purpose), used to connect a verb to a following clause. It means "in order to", "for the purpose of", or "so as to" and expresses the speaker's intention or purpose behind an action. It is more formal and literary than ために or ように, and is commonly found in written Japanese, formal speeches, news articles, and business contexts.
べく attaches to the dictionary form of verbs:
Note: With する, both するべく and すべく are used, but すべく is the more traditional and common form.
べく expresses that someone performs the action in the main clause with the purpose of achieving what is stated before べく. The subject of both clauses is typically the same person.
Both express purpose, but べく carries a stronger sense of determination, resolve, or formality. It is rarely used in casual conversation. Compare:
This sounds more determined and literary than 合格するために勉強した.
The expression べくして is used in the set phrase ~べくしてなる/~べくしてなった, meaning something happened as it was destined to or as was meant to be.