30) Determine if the following is divergent or convergent. If it is convergent, find its sum. 8 +.. 5' 25 ' 125 4 |

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

Q: Find the Value of p which intagral the Converges, abso leste ly Cosn du- Conditionaly. to Jean de

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

Q: 00 Σ n(Inn) n=2

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Q: What is true for the sequence of general terma, =1+(-1)" ? Select one: O converges to 2 O None of…

A:

Q: By 6/2silon definition, check the Convergenre of the following Sequenies. = 2n21

A: Given that, Sn=2n2+12n2-1 We find the limit of this sequence as follows:…

Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

A:

Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: Decide whether the following converges or diverges. 1 En=1 Inn+n!/2 100

A: Given series is ∑n=1∞1lnn+n Let xn=lnn+n Now, for n≥1,  lnn<nn+lnn<2n12n<1n+lnn Let us…

Q: la) 을 In ? n=2 16) n=2

A: The solution of given problem is given as follows :

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: 1 ·d. -? (r+1)2

A: We have to calculate the given definite integral according to the given information

Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

A:

Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: 3. Sn = + + ...+ Show that the {sn} sequence given in general terms converges %3D

A:

Q: Determine the rate of convergence of the sequence an = sin( as n + 00. A. O(1/n) B. O(n) OC.…

A: given sequence an=sin2n+3n2-5  to find the rate of convergence of sequence as n→∞

Q: 6. Use e 6 delinition and prove that he soquence, baving general term converges to 3.

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Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e

A: Option 3 is correct.

Q: Determine whether the following sequence converges or diverges. If it converges, find 3" where n >…

A: The given sequence is: an=3nn! ;           where  n≥1

Q: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

Q: +oo Σ 8n2 16n + 6

A:

Q: Use the integral test to find whether the following series converge or diverge. Hint and warTing: Do…

A: We will check the convergence of given series using integral test.

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: Find Sn for the serks n= Does the seres converge ?

A: Consider the given series. Sn=∑n=1∞1n+3-1n+4 Expend the series and find the limit…

Q: of the given improper in tegrals convergent. are sinz da 1. ース? de

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Q: Show that the sequence {fn} where fu(r) = e-n* is uniformly convergent on [a, b), a > 0.

A:

Q: Use the Limit Comparison Test to determine whether converges or diverges. Vnvn +1 n=1

A: we have to test whether the given series is convergent or divergent by limit comparison test

Q: H) IM:

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Q: 2 n 1 o Show that + converges/diverges n-

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Q: Determine if the sequence converges or diverges. If it converges, state the limit. arctan n -,n≥2 In…

A:

Q: 2. . For each of the following SEQUENCES, determ converges, find the limit. (GIVE REASONS FOR for…

A: a.   an=1+0.7nb.   an=nlnn n=2,3,4,...

Q: +00 n! と+1 n=1

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: Find the smallest positive integer n so that S, approximates the sum of the convergent ser to four…

A: Here we have to find the smallest positive integer n so so the Sn, approximates the sum of the…

Q: (-1)r+1 Vn + 1 n+ 1 10. -1)n+1, N=1

A:

Q: etermine whether the following is convergent or divergent and j

A: Given that,

Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n&gt;0 and then we show…

Q: 1 Determine if dr converges or diverges. If convergent, find its value. (In r21

A: Given: ∫0∞1x1+ln x2dx

Q: The sequence Converges to e Diverges Converges to 2e Converges to 1 Converges to 0

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Q: 1

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Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: +00 3 E(-1)"+1, n n=1

A:

Q: Q. By c/2silon definition , check the convergenie of fallowing sequenies the =

A:

Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to

A: We have to solve

Q: Note: If it converges, consider whether it is geometric or telescoping and enter its sum. If it…

A:

Q: The sequence (Xn) = (1, 3, 1, 3, 1, . . . , 1, 3, ...) is: Converge to 3. O Divergent. Converge to 0…

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Q: 8. Suppose ar > 0 and Does > ak converge or k diverge? Why? %3D

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Q: Use the integral test to find whether the following series converge or diverge. Hint and waTTirg: Do…

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Q: The series is convergent to 21 divergent convergent to 3 convergent to None 1/2 3/5

A: Topic- convergence and divergence of series

Q: Determine if the following is convergent or divergent: I dr

A: