(a) If for each k 23. Suppose (An) are events. show (d) Show iff VRHUT n-1 EP(An (A) = 00, n=k i=k (b) What is the relevance to the Borel Zero-One Law? (c) Is it enough to assume P(lim sup An) = 1. 818 n-1 ΣP(A₁lAj) = ∞o? i=1 n=1 P (lim sup An) = 1 84x

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A: Ephelon delta definition of the limit

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A: I have used only one formula of euler phi function

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A:

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A:

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A: For  satisfying ,  using the binomail theorem.

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A: We  need to evaluate the limitlimn→∞6n+143n+11

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A: I am attaching image so that you understand each and every step.

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A: Dear student, If you find this solution helpful please upvote ? it.

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A: Explanation of the answer is as follows

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A:

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A: Given: To determine: L(25)

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A: To show that limn→∞ n!n=∞

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A: This is a question of topology.

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A:

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A:

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A: Riemann zeta function is a complex-valued function defined as ςs=∑n=1∞1ns.  There is a relationship…

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A:

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A: Given: Let us show the combinatorial proofs of the following identities a) n2=2n-1-1 b) nn-1=n2 c)…

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A:

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A: We have to find limn→∞-1nn+5

Q: 1. Suppose that for a certain life , S×(x) =1- 100 Find (i) Find the prob. that a person aged 25…

A: Given problem is :

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A:

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A:

Q: Find the limits

A: Apply the limits to the function. limx→2x2-7x+10x-2=22-7×2+102-2=4-14+100=00

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A:

Q: 1. Suppose that for a certain life , S, (x) = 1- . Find 100 (i) Find the prob. that a person aged 25…

A: Given : The survival function for a certain life is : SXx=1-x1002

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A:

Q: 9. Let p be an odd prime, and let ( - 1)(a – 2).. (a - (p - 1)) = "--g12-2 -3 -...+ ap-32 - p-2a +…

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A:

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A:

Q: (9) Show that the given collection F is an open cover for S such that it does not contain a finite…

A: (9) (a) Given that S = 0, 2 and F = Un | n∈ℕ where Un = 1n, 2-1n. The objective is to show that the…

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A: To find the supremum and infimum of the sequence S .