Suppose that {a;} is a Cauchy sequence in a metric space X, d and lim an = p. Suppose, in addition, {bi} is a sequence such that n-00 1 d(an, bn) < for all positive integers n. Prove that lim bn = p. %3D n-00

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A: 3.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.