Let A denote the set of subsequential limits of a sequence {an}n≥1. Suppose that {bn}n≥1 is a subsequence in A ∩ R such that lim bn exists in R ∪ {±∞}. Show that limbn belongs to A.

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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.