Nth \ENTH\ , adjective;
1. Being the last in a series of infinitely decreasing or increasing values, amounts, etc.
2. (Of an item in a series of occurrences, planned events, things used, etc., that is thought of as being infinitely large) being the latest, or most recent
According to Etymonline.com:
Dating to 1852, the phrase to the nth is a figurative application of a mathematical term indicating an indefinite number. N is an abbreviation for number.
*Today's word and the first definition were both taken from Dictionary.com's 'Word of the Day' for Sunday, December 19
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