26. (Barndorff-Nielsen) Suppose {En} is a sequence of events such that lim_ P(En) = 0, ΣP(EnE+1) < 0. Prove n P(En i.o.) = 0. Hint: Decompose Un Ej for m > n. j=n

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A:

Q: 18. Which of these sequences is/are not bounded? I. a, = (-1)", n> 1 А. II only В. I only С. П only.…

A: Option (C) is correct. II only.

Q: 28. (Continuation of Exercise 27.) If E=1an converges, and if 1 > a, > 0 for all n, show that E=1 In…

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A: Consider a sequence, Sn, with lim sup Sn = 10 and lim inf Sn = 5. (a) To show that Sn is bounded. By…

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Q: 1 a) Sn+1 = 3 – Sn 25, -35m b) Sn+1 Sn-1 9Sn c) Sn+1 S+1

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Q: 17. Let (Hn) be a sequence defined by Hn k' k=1 1 0, n +1 (b) Deduce that In(n + 1) < Hn < Inn+1…

A: Note: Since we can solve first three subparts of a question, we have solved the first three…

Q: 7. Use the ratio test for sequences to prove that limn→∞ n¹/n² = : 1.

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A: Given: Let's say there are two bounded sequences (an, bn) .a. Demonstrate that limn→∞sup max(an,…

Q: why cant an expert solve this? please help

A: Step 1:To prove this inequality, let's first understand what limsup and liminf mean.limsup (limit…

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Q: 10. Suppose (an}, {bn} are sequences of nonnegative real numbers with him bn = b = 0 and lim a, = a.…

A: 10. Given that are sequence of nonnegative real numbers with        and       To prove that:

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A: For a vector space X, over a field F, a normed linear space X,· is referred to as Banach space if…

Q: == 2.9 Let (an) be a sequence with limit a, and define bɲ = an+1 (n = 1, 2,...). Show that (bn) → a.

A: We know that  A sequence an converges to a limit L  if, for any positive real number epsilon there…

Q: 3. Prove that if (a, } and (b,} are Cauchy sequences of rational numbers satisfying lim (a, - b, = 0…

A: 3.

Q: (-1)" . 2n 4 – 5n (-1)" · 2

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A: This question related to sequence from real analysis.

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A: Cauchy sequence

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