1530s, "provision for support of a retainer; manner of social behavior," now obsolete, along with other 16c. senses; from entertain + -ment. Meaning "the amusement of someone" is from 1610s; sense of "that which entertains" is from 1650s; that of "public performance or display meant to amuse" is from 1727.
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<a href="https://www.etymonline.com/word/infotainment">Etymology of infotainment by etymonline</a>
Harper, D. (n.d.). Etymology of infotainment. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/infotainment