Let f:with input D produces output Real numbers. Let x1 be an accumulation point of D.  Then f has a limit (L) at x1 if and only if for every sequence {xn} converging to x1 with xn in D, (xn not equal to x1) for all n, the sequence {f(xn)} converges.  I understand that this is a way to prove a limit of a function, that this uses sequences to prove a limit of a function. Your help is appreciated . Please be complete in your explanations.  Thank you.

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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.