25. Which of the following series conditionally converges (−1)²+¹ (-1)" 4 n √n 1.Σ n=1 1 1. Σ III. Σ n=1 n=1 n

Q: ) For what values of x do the following power series converge? G(r) = (* - 2)" n5" n=1

A: By the ratio test Let an =(x-2)n/(n5n)      |an+1|/|an| =|(x-2)n+1/((n+1)5n+1)|/|(x-2)n/(n5n)|…

Q: Which of the following series converge? 1 (1) E e n= 100 n 100 (II) (1) Σ 0.99999 n=1 n - 1.00001…

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Q: 1. ส IME IM8 IM8 (cos(n)) ln(n) 2.(-1)". 3. √n n+ 9 n + ln(n) 12 – 7

A: According to bartlby answering guidelines we can only answers three sub parts of a question…

Q: which of the following series are not convergent? Select one: a. Lk-0 , sin(kt) O b. Ek-0 55t1 O c.…

A: As per the question, we need to find one series which is not convergent. Let us start from option…

Q: Σε ≡ the series Σ (-1) ¹2" n! n=1 or divergent? Justify your answer. absolutely convergent, C

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Q: Q.2\ The series E is n(1+ln(n))

A: ∑n=1∞1n1+lnn

Q: 2. For each of the following series, justify briefly why it is divergent. a. E* n+2

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

Q: 2+1 S X77(1) 1=2 M2

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Q: Which of the following series converge absolutely, which converge conditionally, and which diverge?

A: Given  1. ∑n=2∞-1nnn3-52. ∑n=0∞-1nn2+1n2+n+83. ∑n=1∞-1n74-5nn

Q: Σ (-1)"+1 n³+1 n=0

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Q: Which of the following series is convergent? Select one: 72 5n A. 2n + 3 n=1 3n ов. 2n + 5 n=1 72 2n…

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Q: 4. Determine whether the following series converges or not. n=1 1 2n+1+√3n-2

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Q: 10. Find the values of x for which the following power series converge: (a) nkan for k an integer.…

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Q: Σ 22η n=1

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Q: Which of the following series diverges? a. an 3n b. an = e-n an = (-0.32)" d. an = (-0.4)-n %3D

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Q: 3. Investigate and decide whether the following series are convergent: 3n+1n2 Σ n + 3 Σ' 67 3n2

A: We'll answer the first question since the exact one wasn't specified.  Please submit a new question…

Q: 8. Which ön ing series is convergent? A. E(1-r)" B. Er(1+r) 3" D. r=0

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Q: For each of the given series, determine if it converges or not. Give reasons for your answer. If it…

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Q: 4. Consider the following tests: n-th Term , Integral, Direct Comparison, Limit Comparison, Ratio,…

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Q: (-9)" (2n)! n=0 (a)e³ (b) cos 3 (c) co (d) sin 3 (e) None

A: The given series is ∑n=0∞(-9)n(2n)!

Q: 1. Σ-1)"n 1 (n + 3 ) 00 n5 2. 6 – 9n3 (п +7)" 3. 5" (9 + n)5"

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Q: 11. Find the partial sum of the following series using the first five terms and determine the error…

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