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In: Advanced Math

4.2.1. Problem. Suppose that (xn) and (yn) are sequences of real numbers, that xn → a...

4.2.1. Problem. Suppose that (xn) and (yn) are sequences of real numbers, that xn → a and yn → b, and that c ∈ R. For the case where a and b are real numbers derive the following:
(a) xn +yn →a+b,
(b) xn −yn →a−b,
(c) xnyn → ab,
(d) cxn → ca,
(e) xn/yn → a/b if b ̸= 0.

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