13. Which of the following statements is/are false? I. En1 ar"-1 is divergent if |r| > 1 convergent if p<1 +00 II. E is nP -n=1 an+1 III. E an, where a, + 0, is convergent if lim < 1 an n→+00 A. I only B. II and III C. I and II D. I, II and III

Q: Ex 11.1.3 Determine whether {Vn 47 n converges or diverges. If it converges compute the limit.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Question 2. (20 marks) Let (zn)n be the sequence of real numbers defined by 1 = √2, n+1 = √n+2, neN.…

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Q: 3 an +2 A sequence of real numbers a, is defines inductively as a, = 1 and an+1 = n2 1. %3D an +3…

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Q: 1.8.7.) (a) Let an and b, be real or complex numbers. Show that if Yn and bn each converge, then E…

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Q: 2.J Let fn(x) = x ½n for 0<x< 1 and neN. or.) Find a function f on [at] such that (fr) converges.…

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Q: 65. Suppose that the coefficients of F(x) = anx" are periodic; that is, for some whole number M > 0,…

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Q: Q 5. For -∞0 < x <∞, define -{ Show that f is not continuous at z = 0. [Hint: Use sequences.] f(x) =…

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Q: Label the following statements as true (T) or false (F). lim, 00 (4n² – 5n) = e If lim,-00 an = 0,…

A: (a)

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Q: 7.a) Rank the following time bounds. That is write them as f₁, f2, ..., f6 and show that fi =…

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Q: 4. Let TN → N be an injective function. Prove that if {n}1 converges to x, then {*T(n)} also…

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Q: 25. Let a, := (), n2 1. Which of these conditions must be met if a, is to converge n+1 to 1? I for…

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Q: 12. For each n € N, define An = [0,1 + ½] and B₂ = [0, 1 − 1]. - (a) Prove that Uº₁ An is an…

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Q: .8.8 Suppose that Cn >0 for each n E N. Prove that n either converges = diverges to infinity.

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Q: Ex 11.1.1 Compute lim r

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the limit of the following sequences or show why they diverge. n2 – 2n + 1 (a) - en n+ (b)

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Q: 25. Let an := n 2 1. Which of these conditions must be met if a, is to converge n+1 to 1? I. for any…

A: Just use definition of convergence.

Q: 1. Suppose for all n, an and bn are positive. If lim n-x Σan = 6 then Σαπ n=1 n=1 bn is also…

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Q: n! converges. Hint: Use lim Show that = e. пh п-1

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