9. Which of the following is/are correct? I. If is a positive convergent series, is convergent too. 80 II. If is a positive convergent series, is divergent. III. The series is convergent for p = 2. (Inn)P A) I only B) II only C) III only D) I and III E) I, Il and III

Q: 4 10. ΣΕ1 %3D1 k In? k 2.

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Q: Determine the convergence or divergence of the series

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Q: If L uk and > Uk are convergent series, then > (uk + Vk) and Συ 2(uk – vk) are convergent series and…

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Q: Let Ean and Eb, be series with non-negative terms. If a, > b, for all n > 1 and b, converges, then…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2. Determine whether the following series is convergent or divergent: (4n)²n evnn2n n=1

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Q: 4. Study the convergence of the series In(1+ ) Inn n=2 and In(1+ ;) (In n)2 n=2

A: Observe the following inequality: 12n<1n+1≤ln1+1n for natural numbers , n≥2. ⇒1(2n) ln…

Q: If > uk and > v% are convergent series, then > (uk + v%) and 2(uk – Vk) are convergent series and…

A: First we take partially fraction then we use sum of GP.

Q: Determine whether the series is (are) converge(s) absolutely. 3* -1 A and D C and D None A and C

A: Solution is given as below:

Q: 3. Which of the following series converge and which diverge?

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Q: Determine whether the following series is convergent or divergent: (4n)2n evnn2n n=1

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Q: 15. Use the ratio test or root test to determine whether the series below converges or diverges. п!…

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Q: Use an appropriate test to determine whether the series converges. Σ k=1 By the 9 k 12 9 this series

A: Please see the below picture for detailed solution.

Q: 7. Determine if the following infinite series are absolutely convergent, conditionally con- vergent…

A: Given series is ∑n=1∞4n5n+3 According to the divergence test, if the limit of given series is not…

Q: Consider the series 2 ark 1, a +0. Then if r|< 1, the series converges to. Select one: O a. None of…

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Q: 2) Use a comparison test to determine whether the infinite series S n2 n+ n2+ n5/2 converges or…

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Q: 4) Let Eanbe given series and let Eb, be series in which the terms are the same order as in Ean…

A: Given- Let ∑an be given series and let ∑bn be the series in which the terms are the same order as in…

Q: In the root test if p>1 than the series is diverges O True false

A: In this question, we need to find whether the given statement is true or false.

Q: Determine whether the series is convergent or diverg In(n) Σ 8 n = 1 8.

A: We will do Ratio test.

Q: 3. Prove that the following series are neither converges nor diverges using mathematical approach. 1…

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Q: vn 8. En=1 73

A: We have to determine whether the given series is convergent or divergent.

Q: Determine if the series 1/n14 , n = 1 to infinity converges or diverges. Explain.

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Q: 32. Show if the series converges or diverges using the Alternating Series test 00 1n+1 Vn n=1

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Q: 2. Use root test to determine whether the following series is convergent or divergent: 00 Σ n=2…

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Q: The series from n=15 to infinity of n*(-6)^n/n! , does it converge absolutely, conditionally,…

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Q: If the series an , and E (an + b,) are convergent series then b, may be a divergent series. Select…

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Q: 4. Suppose that un 20 and t'n 20 for every n E N. Suppose further that un/Va - Show that the series-…

A: The solution are next step

Q: Determine the convergence or divergence of the series.

A: Consider the given series ∑n=1∞n3n2+3

Q: 5. Determine the sum of the following convergent series 1 (In 3)", n-1

A: Sum of infinite GP with first term a  and common ratio r is given by, Sn = a/(1 - r) for |r|&lt;1

Q: 3 Derermine whether the series. is absolutely Cooecgint, Conditionally convergent, ordivergedt. A…

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Q: 7. Determine if the series converges. If it converges, find the sum: 3n-1+2 En=1 5"

A: ∑n=1∞3n-1+25n=∑n=1∞3n-15n+∑n=1∞25n=13∑n=1∞3n5n+2∑n=1∞15n=13∑n=1∞35n+2∑n=1∞15n∑n=1∞35n is a geometric…

Q: Determine whether the following series is convergent or divergent: Σ (4n)²n evnn2n n=1

A: Series convergence  or divergence

Q: 11 Does the following alternating series converge or diverge? If it converges, does it converge…

A: In the question we have to find whether the series converge or diverge also absolute value.

Q: # 2) Determine if these series converge or diverge. Guesses are PROHIBITED! 00 Α) Σ n=1l (6n+7)

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Q: in 6.7

A: Interval of convergence.

Q: 8. The following series converges. To what does it converge? (i.e., Find the sum of the series.)

A: Given: The series is ∑n= 0∞ 3n10n+2 .

Q: Determine if the following series converges or diverges. If it is a converging geometric or…

A: The series is .

Q: į" 2"(n+1): 3" - n! п-2 Σ 3" 'n²2" WI

A: Definition used-           Ratio test -                L=limn→∞an+1an               If L&lt;1…

Q: 1. Determine if the series is convergent or divergent. (Circle one and give your reason.) (-1)" а.…

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Q: 9.) Determine the convergence or divergence of the series (-1)*+' In(n + 1) n + 1

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Q: If E Uk and > vk are convergent series, then > (uk + vk) and (u – vk) are convergent series and the…

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Q: 1 Study the convergence of the series 'n In(n + 1)

A: Since (n+1)lnn+1&gt;n lnn+1 Therefore 1(n+1)lnn+1&lt;1nlnn+1 But the series ∑n=2∞1nlnn diverges.

Q: 3. Determine whether the given series converges or diverges. If converges, find its sum en n=1

A: Here, we test the convergence of the series by D' Alembert ratio test .

Q: Does the series from n=1 to infinity of (-1)^n*(n+1/n) conditionally converge, absolutely converge,…

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Q: Consider the series Σ In n+5 Determine whether the series converges, and if it converges, determine…

A: Consider the given series. S=∑n=1∞lnnn+5 Now, apply the ratio test. limn→∞an+1an=L

Q: (-1)n+1 In=1 n3 9. Justify that the series converges. Then justify if the series converges…

A: Solution of the problem as follows

Q: Determine the convergence or divergence of the series

A: Given: A series ∑n=1∞ln1n To determine the convergence or divergence take the limit of ln1nfor n→∞…

Q: Determine the convergence or divergence of the series

A: Given: The series is ∑n=2∞nln n.

Q: Consider the series , ark1, a 0. Then if r < 1, the series converges to

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Q: Use an appropriate test to determine whether the series converges. 9 3 Ink M8 Σ k=3 By the this…

A: Comparison test to check the convergence