If a sequence <S> is convergent, then it is
(a) a Cauchy sequence
(b)not a Cauchy sequence
(c) may or may not be a Cauchy sequence
(d) none of these
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So, for any index n and distance d, there exists an index m big enough such that am – an > d. (Actually, any m > (√n + d)2 suffices.) As a result, despite how far one goes, the remaining terms of the sequence never get close to each other, hence the sequence is not Cauchy.
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