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A series is convergent to a number x iff for ε>0, Ε a term of the series, y, such that |x-y| < ε.
Additionally, for a sufficiently large term of the series, y, and the previous term, z, |z-x|>|z-y| is satified
Con*ver"gent (?), a. [Cf. F. convergent.]
Tending to one point of focus; tending to approach each other; converging.
As many rays of light, as conveniently can be let in, and made convergent. Boyle.
The vast dome of its cathedral . . . directing its convergent curves to heaven. Hallam.
© Webster 1913.
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