A sequence {an} is given by its general term 32 1 22 n2 an %3D ... 3n3 3n3 3n3 3n3 Then the limit of the sequence {an} is: Hint : 1+2² +3² + ---+ n? n(n + 1)(2n + 1) 6. O 1/12 and the sequence is convergent. O 1/9 and the sequence is convergent. 1/6 and the sequence is convergent. infinity and the sequence is divergent.

Q: Find the limit of the following sequence or determine that the sequence diverges. {(3n3-1)/(2n3 +…

A: We need to find the limit of {(3n3-1)/(2n3 + 1)} as n tends to infinity. If limit turns out to be 0,…

Q: (a) Find a formula for the general term an of the sequence 8 3 4 4' 9 - } assuming that the pattern…

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Q: 2) (a) What does the sequence defined by x, = 1, and x, =1+ 2 converge to? (Hint: Consider the…

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Q: 3. Divergent or convergent sequences. For each of the sequences below, enter either di- verges if…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: = 1. Find the general term of the sequence, starting with n = Determine whether the sequence…

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Q: Find the limit of the sequence (an if it converges; otherwise indicate it diverges. an = (-1)" 5 O5…

A: Given: an=(-1)n5n   To find: limn→∞an

Q: 4.W: Which of the sequences {an} converge and which diverge: 1-n 3 n+(-1)" 2. an 1. an 70- 4n2

A: Convergence and divergence of the sequence

Q: 12 5n The sequence 1+ 5n n=1 Converges to

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Q: 7n² + 2n 1. Consider the sequence an = 3+11n2 +5n4 (a) Does the sequence {an} converge or diverge?…

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Q: 4. If ak is a nonnegative sequence and E,ak converges then 2k=1@ki aki subsequence of a. 5. If Eak…

A: 4.it is true ,since

Q: Evaluate the limit of the sequence or state that it does not exist. an = (-1)n (3n3 + 4n)/(6n3 + 5)

A: Given sequence: an=(-1)n(3n3+4n)(6n3+5) To find the limit of this given sequence:…

Q: 2. Determine if the given sequence converges or diverges. If it converges, what is its limit? (a) {…

A: Given sequences: 5+3n32n2-6n+5n=0∞9n4+6n26n4-5n2+9n=6∞-1n+72-8nn2+9n=2∞ If we say that a sequence…

Q: 3 4 N + 1 5) Show that the sequence 7 2N + 1 is bounded and monotonic.

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Q: Find the limit of the sequence whose terms are given by: a-sub-n = (e^(2n) + 6n)^(1/n)

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Q: Which of the followings are true? is a decreasing sequence. 1. . n²–1 is not a bounded sequence. II.…

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Q: (Α True B False If the sequence {a}₁, is convergent, then the sequence {x} defined by…

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Q: 3. Let an be the sequence defined by a1 = 1 and an for - ... n > 1. (a) Calculate the first four…

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Q: A True B False If the sequence {a}, is convergent, then the sequence {x} defined by…

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Q: (-9)"+1 Let an 10n Determine whether the sequence {an} is convergent or divergent. If it is…

A: an=(-9)n+110n A sequence is convergent if value of limit is define and finite as n approaches to…

Q: = 1. Find the general term of the sequence, starting with n = Determine whether the sequence…

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Q: Find if the sequences diverges or converges. If converegs, find the limit. 1. an=n1/n

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

Q: 2n4+25n2+32n-15 The nth term of a sequence is represented by 6n4+2n3 –11n²–2n+17 What is the limit…

A: Find the limit of the function where n tends to infinity.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: Topic:- sequence and series

Q: Find the general term of the sequence, starting with n 1,determine whether the sequence converges,…

A: We have to start with n=1 to make given sequence. we have to find an and limit value

Q: 4. Consider the sequence {n} (a) Write out the first five terms of the sequence (b) Determine…

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Q: 2πη? + eπ (b) Find the limit of the sequence {² converges. Otherwise, state that the sequence…

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: This is problem of sequence calculation. Based on the general formula and test available we will…

Q: A sequence {an} is given by its general term 32 22 1 an n2 ... 3n3 3n3 3n3 3n3 Then the limit of the…

A: We have to find limit value of sequence after that we have to check weather the given series is…

Q: Find the limit of the sequence: In? + 1n + 3 an 9n2 + 8n + 1

A: Question is solved.

Q: = (a) Compute the limit of the sequence with general term an (b) Write Σn=1 n(n+3) 1 as a telescopic…

A: we can find the limit of the sequence . Note : As per our guidelines , we can solve first one as…

Q: 1 N. 3 n + 2 (a) Find the smallest positive integer N such that Зп — 4 n2 (b) Determine whether the…

A: To find: Smallest positive integer N such that n+23n-4-13<0.01. for all n≥N. As per policy, we…

Q: 19. Find the limit of the convergent sequence defined recursively by the equations * a = 2 An+1 = 2…

A: Solve the following

Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence…

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Q: (5n + 1)! Find the limit of the sequence an = If the limit does not exist, type "Diverges" or "D".…

A: We know, (5n+1)! = (5n+1)5n(5n-1)! So, (5n+1)!/(5n-1)! = 5n(5n+1) So, an = 5n(5n+1) = 25n² + 5n

Q: Q: Determine if the following sequences converge or diverge. If the sequence converges determine its…

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

Q: (c) Find the limit of the sequence {In(5n³ − n + 1) − ln(7n³ − n +1)} if it converges. Otherwise,…

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Q: -3 n 1+ 8 n Find the limit of the sequence an = If the limit does not exist, type "Diverges" or "D".…

A: Topic = Limits if limn→∞an=finite ⇒Converseif limn→∞an→∞ ⇒diverse

Q: What test would you use to test the convergenc 2n+1 n=1 n³-4n²+6 2. ΣΤ-1 (-1)"+1 (n²+3)² 3. Σ-1 5sec…

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Q: 5 2n Determine if the sequence {4} converges or diverges. If it converges, find its limit: 3n 7…

A: To determine the limit of the sequence.

Q: { 2 An – 4 converges to 7, then the - If the sequence An + 2 sequence {an} converges to 9.

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Q: 1. Let r = 0.5 and choose xo = 0.2. Either by hand or by using a computer, calculate the first 10…

A: Step 1: Plot the function f(x)=r·x·(1-x) and line y=x on the same graph. Step 2: Mark the point (x0…

Q: Find the limit of the following sequence or determine that the sequence diverges. {ln (n3 + 1) - ln…

A: an=lnn3+1-ln3n3+10n

Q: (-1)*+a 2 4. Determine if converges. 2n - 5 (n +1)² + 5

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Q: 3n 2. Find the first 6 terms of the sequence defined by an = n+1 Does it have a limit? n² + 4n + 5…

A: Consider the sequence,

Q: 7. Determine whether the sequence defined by a, = 5+2(-1)" converges or diverges. If it converges,…

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Q: (-1)"n For positive integer n, let an = 3n (a) Determine whether the sequence {an} is convergent. 00…

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Q: 4n an n a) Is the sequence bounded? If yes, then find the bound. b) Is the sequence increasing,…

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Q: 2 4 N + 1 5) Show that the sequence 2N + ... ... is bounded and monotonic.

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Q: Determine the limit of the sequence or show that the sequence diverges. If it converges, find its…

A: We have to determine the limit of the sequence.

Q: 19. Find the limit of the convergent sequence defined recursively by the equations * s) 2 = 12 an+1…

A: Explanation of the answer is as follows