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From: Webster's Revised Unabridged Dictionary (1913)

 Con·ver·ging a. Tending to one point; approaching each other; convergent; as, converging lines.
 Converging raysOpt., rays of light, which, proceeding from different points of an object, tend toward a single point.
 Converging series Math., a series in which if an indefinitely great number of terms be taken, their sum will become indefinitely near in value to a fixed quantity, which is called the sum of the series; -- opposed to a diverging series.