00 Σα Σα ? 28. Given that converges to L, which conclusion is valid for a n= n-1 A) It converges to L B) It may diverge C) It converges absolutely D) It converges to M < L E) It converges to M > L. the X X

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A: It can be obtained by using limit evaluation of the given sequence

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A: We will prove that if { sn } converges then {|sn|} also converges.

Q: Question A.) Does this CONVERGE or DIVERGE? er 2 (lan) ² W nal

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Q: Is the sequen ce in (R.To)? (0,1.0.1.0,1,..) convergent Prove the answer

A: It is given that the topology space ℝ,τ0. Here, τ0=ℝ,∅. That is, the open sets of ℝ  are ℝ and ∅.…

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Q: Suppose ak > 0 and there exists M >0 so that E ak < M for all n E N. Prove that ak converges. k=n…

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Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

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Q: (j) F= R, V = {vER: Un converges as n → ∞0}; (k) F= R, V = {v ER: un converges absolutely as n→ ∞0};…

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Q: ounded funclions on A to h,t converges uniformly

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Q: plz ans both B and C

A: This method is called power method. If modulus of all eigen values less than 1 then the power method…

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Q: Which of the following statements is equivalent to Theorem 1? 8. A.lf a, diverges, then a, also…

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Q: MEDI is a) converges to 2 b) converges to 2/2 c) converges to 23 d) diverges e) None of all

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Q: 13.D. Show that, if we define fn on R by fa (x) 1+ n?x? then (fn) converges on R.

A: givenfn(x)=nx1+n2x2dividing numerator and denominator by x2fn(x)=nxx21+n2x2x2

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Q: a) Show by example that E( an /b.) may diverge even thagh E an and E bn converge and no b, equals 0.

A: Since solve the first question for you. If youwant any specific question to be solved then please…

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Q: let E an3 be a segence defined recurs ively by An=1 , anti=Jl+5an, n=l,2,3. Suppose that Does { 9n3…

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Q: 16) If E an converges, then cos(am) diverges. n=1 n=1 a) True b) False

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: Given: a, = In(n + 1) – In(n) for n e N Determine if the following is convergent or divergent. (a)…

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Q: 5. Let h, : [0, o∞) → R be given by h„(x) and let h : [0, ∞) → R be given by I +n %3D h(x) = = x.…

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Q: If lim M→0 J1 rM dx converges, then which of the xP Following must be true? elect one: o a. Σ…

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Q: Q 12.11 whot values of does this Seirics seines converge? n (in u) n=2

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Q: determine the domain AND the function to converge the serie e converge la serie: E=0 Re(u). n%3D0

A: Consider the given series

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A: Let (an) is increasing sequence and converges to a,

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A: here option (B) is true this is converges for p&gt;=1

Q: 3. Let {fn}n=1 and {gn}-1 converges uniformly on E. Prove that {fn - In}n=1 converge uniformly on E.

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Q: (a) Prove that 4280 k!pk k=0 converges for any r > 0.

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Q: T or F , prove your answer Suppose (an) is Cauchy and that for every n ∈ N, the interval (−1/n,…

A: Statement is TRUE By the ARCHIMEDEAN PROPERTY AND DEFINITION OF LIMIT.

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Q: Let f(x) = a,x",g(x)=b,x". Suppose both series converge for |x| < R. Let n=0 n=0 x, be a number such…

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Q: Let {fn}n=1 and {gn}n=1 converges uniformly on E. Prove that {fr – In}=1 converge uniformly on E.

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Q: (iv) We say {fn} converges uniformly to f(x) iff (Ve > 0)(3n > 0)(Væ)(n >n=\fn(x) – f(z)| < c). What…

A: (Part 4 ) only asked and answered

Q: (b) Use the Weierstrass M-test to show that E(cos.x)". 4 n=0 converges uniformly on [A/4, 37/4].

A: The series is given by: ∑n=0∞cos x2n,    x∈π4,3π4 Now, ∑a2n=a0+a2+a4+... Now, cos function lies…

Q: b) Prove that sin z is unbounded in {z E C: |Re z|< 1}. c) Prove that sin- is uniformly convergent…

A: We have to solve given questions.

Q: a) Show by example thiat E(an /b, ) mey diverge even thagh E an 4nd E b, converge and no b, equak 0.…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…