being the last in a series of infinitely decreasing or increasing values, amounts, etc.
(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: This is the nth time I've told you to eat slowly.
the nth degree/power,
a high degree or power.
the utmost degree or extent: The new hotel was luxurious to the nth degree.