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  3. let (xn), (yn) be bounded sequences. a) prove that

Let (xn), (yn) be bounded sequences. a) Prove that lim inf xn + lim inf yn...

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Advance Math

Let (xn), (yn) be bounded sequences.

a) Prove that lim inf xn + lim inf yn ?lim inf(xn + yn) ? lim sup(xn +yn) ? lim sup xn + lim sup yn.Give example where all inequalities are strict.

b)Let (zn) be the sequence defined recursively byz1 = z2 = 1, zn+2 = ?zn+1 + ? zn, n = 1, 2, . . . . Prove that(zn) is convergent and find its limit. Hint; argue that0 < zn < 4 for all n and use part (a).

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