4. Consider a power series of the form E anx". Suppose that lim sup Jan|/n = 0. Prove that the series anx" converges for all x E R.

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Q: 2" + 3" (a) Show that the series converges. 4" + 5" k2 k=1 n=1

A: Note: According to bartleby we have to solve the first question please upload the question…

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Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows

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A: Find the interval of convergence of the series

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A: To solve the following problem and find the interval of convergence

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Q: Find an easy expression for the sum of the series on its interval of convergence. (-1)"-'n -x" 2"…

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Q: a) Find the length of the curve y = 5x/T - 6, 1<r< 3.

A: Arc length of the curve along x-axis

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Q: Q1. Test for conditionally converge, Absolutely converge, or diverge of the series E(-1)"

A: The  series of the form∑n=1∞an is said to be conditional convergent if the series ∑n=1∞an is…

Q: The series O True O False Σ (-1)^+1 n=2 n3+1 is absolutely convergent.

A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

Q: For which z's does the infinite series 1+ 좋 + + +. zn + . 3" 27 converge? To what function does it…

A: The solution are next step

Q: 3" 29. The series (x-2)" is convergent on the interval: (03) A) 5 7 B) 3 3 5 7 C) 3 3 5 7 D) 5 7 E)…

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Q: (– 1)"(x+2)" What is the interval of convergence for the series 2 n=1 О.[-6,2) O b.(- 6,2] Oc[-6,–…

A: The correct answer is option B. The given series is  ∑n=1∞-1nx+2n4nn The ratio test will be given by…

Q: power series converges at a single a. what is the radius Of ConvergCnC (c) R=0

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Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

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Q: For what values of pisthe series convergent Please answer in

A: Given,           ∑n=2∞(-1)n-1lnnpn3.

Q: For what values of x, the series converges? Σ-1 (In x)"

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A: Option e) is Right option I am providing detailed statement solution below

Q: 1. Is the series convergent En>2 n(Inn)?

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Q: 2. Multi-Step Series E sin(n) n2 а. b. E sin(n) n=1 n² – 5 n=1 -

A: We are authorized to answer one question at a time, since you have not mentioned which question you…