Question: 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

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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