What are all values of r for which the series(-1)+1(r+2)"converges?n=1(A) -1

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Answered: What are all values of r for which the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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please send handwritten solution for Q 34 1.6
Consider the series San where n=1 (-1)"n n² + 2n + 5 In this problem you must attempt to use the Ratio Test to decide whether the series converges. Compute an = an+1 L = lim n-00 an Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, -INF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L = Which of the following statements is true? A. The Ratio Test says that the series converges absolutely. B. The Ratio Test says that the series diverges. C. The Ratio Test says that the series converges conditionally. D. The Ratio Test is inconclusive, but the series converges absolutely by another test or tests. E. The Ratio Test is inconclusive, but the series diverges by another test or tests. F. The Ratio Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:
3 The series E converges if n=2 (n+ 1)P (n – 1)ª - (a) p+q 1 (c) p+q=1 (d) p+q=; 1 (e) -1
2n-1 + Prove that the series 1+ 22 +... converges. .. 33
k! 2. Consider the series We will use the Ratio Test to determine whether this series converges or (2k)!" diverges. k! (a) For this series ak Write down ak+1· (2k)!" ak+1 (b) Determine lim Ak k! converges or diverges. (2k)! (c) Determine whether the series k=1
i need the answer quickly
Expand ? ? =?2(?+2)(?−3)in Laurent’s series if (i) ? < 2 and (ii) 2 < ? < 3
Discrete Math ( Proof)
5. Consider the series n! n=0 for real numbers x. (a) Use the ratio test to determine the values x for which the series is absolutely convergent. (b) Does this mean that the series is convergent for these values of x? Explain. (c) Explain how one can use part (b) above to determine the limit of the sequence {an} where 22n an n!
∞ 1. Let an be a POSITIVE infinite series (i.e. an > 0 for all n ≥ 1). Let ƒ be a continuous function n=1 with domain R. Is each of these statements true or false? If it is true, prove it. If it is false, prove it by providing a counterexample and justify that is satisfies the required conditions.

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What are all values of r for which the series (-1)+1(r+2)" converges? n=1 (A) –1