Suppose that {xn} and {yn} are real sequences. a) Prove that provided that none of these sums
Question:
a) Prove that
provided that none of these sums is of the form ˆž - ˆž.
b) Show that if limn†’ˆž xn exists, then
and
c) Show by examples that each of the inequalities in part (a) can be strict.
Transcribed Image Text:
lim inf xn + lim inf yn lim inn) S lim sup x lim inf y S m sup(n t yn) lim sup+lim sup yn lim inf(x" + yn) = lim xn + lim infy" lim sup(xn+yn) = lim xn +lin supyn
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a Since inf k n x k inf k n y k is a lower bound of x j y j for any j n we have inf k n x k inf ...View the full answer
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