Show that if (xn) and (yn) are bounded sequences, then lim sup(xn + yn) < lim sup(xn)

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Show that if (xn) and (yn) are bounded sequences, then
lim sup(xn + yn) < lim sup(xn) + lim sup(yn):
Give an example in which the two sides are not equal.
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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