Let {xn} from n=1 to n=infinity and {yn} from n=1 to n=infinity be convergent sequences with limits x and y, respectively. Suppose that all the yn's and y are nonzero. Show that the sequence {xn / yn} from n=1 to n=infinity converges to x/y.

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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.