3. Let e be a cluster point of a subset A of R and letf: A+R be a function. Suppose for every sequence (a,) in A such that lim a, = e, the sequence (f(u.)) is a Cauchy sequence. Prove that lim f(x) exists.

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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.