2. Determine the convergence and divergence of the following Sequences: 3" 6" b. (1 -)") c. flan a. 2-n n! (In n)200 72 n4 n2 d. (sin- (E)+ tanh-( } n++8n3

Q: Determine the convergence or divergence of the series. 00 cos(nTt) n = 1 O converges O diverges

A: The correct option is “diverges”. Expand the given series.

Q: In k 4. ek n=1

A: Given Series is Convergent by Using Ratio Test

Q: Determine the convergence or divergence of the series.

A: Now, convert the above series to improper integral.

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: Find the radius and interval of convergence of the series. (л — 2)" 6" In n n=2

A: Given series

Q: Find the radius of convergence of the power series.

A: Given:

Q: Find the interval of convergence of the series. (3x)" 2" n=1

A:

Q: Find the interval of convergence of the series. (5x) n².4" n=1

A: A power series is given by, ∑n = 1∞ 5xnn2·4n. The objective is to find the interval of convergence…

Q: 43. (n!)2 Σ (2n)! n=0

A:

Q: Determine the convergence or divergence of the following series 2 sin³ n n² -1

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

Q: 2. P, = 3¬P-+, n21 is linearly convergent to the limit p. Generate the first four terms of the…

A: Aitken's ∆2 Method:- is based on the assumption that the sequence  p^n defined by…

Q: Find the radius of convergence for: (n!)* (3n)! n=1 1

A: Given :

Q: Q3/ Check the convergence of the following series 2 3(n + 1)(n + 2) n=0 Ans./ Use method of…

A:

Q: 2. Find the interval of convergence for the series. n=1 (x - 7) n n5n

A:

Q: +o0 (-1)*n" sin" () Σ 2n n=1

A:

Q: Σ (d) n (In(n))2

A:

Q: Use the Ratio Test to determine whether the series is convergent or divergent. -1 57 3nn³ 00…

A: To Use: The Ratio Test to determine whether the series is convergent or divergent. ∑n=1∞-1n5n3n n3…

Q: 8. 2) Find the interval of convergence for the powen (n+ 1): (x – 1 n=0

A:

Q: Compute the limit of the nth term and use it to explain why the series is divergent. +00 2" – 1 2 2n…

A:

Q: TON (B) Discuss the convergence of the given sequence: a(n) = sin 2

A:

Q: Using only the Archimedean Property of R give a direct E-N verification of the convergence of the…

A: To prove that the given sequence converges using the Archimedean property of the real number system

Q: Find the radius of convergence of the series: (2п)! (n!)2 n=1

A:

Q: Find the interval of convergence of the series. (5х)" 2" n=1

A:

Q: 2n +1 a) n=1 3n-5 WE

A: Solution:Given  ∑n=1∞ 2n+13n-5To find the nth term test say about the convergence of the series.

Q: 8. Use the fact that ()1 converges to 0 along with the theory derived in this section and worksheet…

A: We can solve this by the help of squeeze theorem and given details

Q: Suppose that a, 20 and b, 2 0 for alln> N where N is an integer. If an lim = 0, what can you…

A: Consider the given: Limit Comparison test:an,bn>0  ∀ n≥Nlimn→∞anbn>0,∑n=1∞an converges then…

Q: (b) Show that the interval of convergence of the series n=1 sest 2-12-1 (4n-3)² is given by

A:

Q: 01: Find the interval of convergence of the following series. 1. E(-1)"( ) 2. Ex 3. E(-1)" nx"

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: tan (x) n' In(n+2) 04: Determine the convergence of A=[0,+). on

A: Let the sum of the series be given by Sn. ⇒Sn=∑n=0∞tan-1(x)x2+n2ln (n+2) un=∑ n=0∞tan-1(x)x2+n2ln…

Q: 1 g) E 2п-1 n=1

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

Q: (-1)"n (xn) = п+2

A:

Q: Find the interval of convergence for the following series. Σ(3) 2η

A:

Q: Q2. Check the convergence of the series 2 tan-1 n=1

A: The given series, ∑n=1∞ tan-11n Integral Test:  If f(x) is a positive, continuous and decreasing…

Q: Let (rn) be a sequence of real numbers. Show that the convergence of (sn) implies theconvergence of…

A: We have to prove that if convergence of (sn) implies the convergence of (|sn|).

Q: Determine the rate of convergence of the sequence an = sin (12) as n 0o. 2 37n 2 n2 1 O A. O(1/n^3)…

A: Given the sequence is αn=sin23n+2n2-1. Find the rate of convergence of the sequence.

Q: 1 – 4x)k Ek=1 k k3

A: In the question we have to find interval of convergence.

Q: The first term of the sequence is x1 = cos(1). The next terms are x2 = x1 or cos(2), whichever is…

A:

Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 701 Discuss the convergence of the given sequence: a(n) = sin- 2

A: Given sequence: a(n)=<an>=sinnπ2

Q: Find the interval of convergence for Σ 5 k?xk+1 ek+1

A:

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

A:

Q: Determine if this sequence converges og diverges: n3/(cos n+ 5n)

A: We have to solve given problem: Concept:

Q: 04: Determine the convergence of tan¹(x) x²+n²In(n+2) , on A = [0, +00).

A: We have to determine the convergence of the given series of functions ;   ∑n=1∞an = ∑n=1∞tan-1xx2+n2…

Q: Q3/ Check the convergence of the following series 2 Σ 3(n + 1)(n + 2) n=0 Ans./ Use method of…

A:

Q: O Discuss the convergence of f,(x)=x + , on A =[0,00).

A:

Q: Determine the rate of convergence of the sequence an sin( +3 as n+ 00. %3D OA O(1/n) O B. O(n) OC…

A: The given sequence is: αn=sin2n+3n2-5    =2n+3n2-5-13!2n+3n2-53+...    =2+3nn1-5n2-13!2n+3n2-53+...…

Q: 4. If > Cn (T + 2)" converges for -5 < x < 1, find the radius of convergence of the series. n=1

A: The given power series is cn(x+2)n , n from 1 to infinity.

Q: 1. Show that the sequence ((nx - - 1/n)e n) converges uniformly on [0, 0). (15 points)

A: