Beneficently is the adverb from beneficent: in a way that helps people or brings about something good. “She gave beneficently” means she gave so as to do good. Like the adjective, it is formal and a little old-fashioned. In everyday English you would say kindly, generously, or in a way that helps. Though actually, do not reach for this word when you only mean “with a good effect.” That idea belongs to beneficially. Beneficently is about the spirit of doing good, not about a result that happens to be useful.