A Moving to another question will save this response. Question 3 k2+k+3 By using The Divergence Test, the sequence 2 k=1 2k2+1 O Converges O May either Converges or Diverges O Diverges

Q: 1 The sequence converges to - 2 /n² – 1 – /n² + n 20 Select one: True O False

A: The sequence 1n2-1-n2+n   converges to -2    we have to check it is true or false.

Q: Which of the sequences {a,} converge and which diverge: n+(-1)" 1. a=

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Q: An. If > an converges for some large k, then so will n=1 n=k Select one: True False

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Q: If 2n=1a, converges, and if a„ # 1 and a,n > 0 for all n, a. Show that E=1a, converges. b. Does…

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Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: or converges conditionally: kl 2) Σ- Sk - k + 4 k +1 k=1

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Q: 5. Find all values of x >0 so that ) converges. 3k k=2

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Q: n+5 a. (xn) = п-5 n² b. (xn) = %3D п3+1

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

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Q: 1 The sequence converges to - 2 n² – 1 - Vn2 +n Select one: O True O False

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Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: In each problem, test for convergence or divergence: n/n Σ (n+1Xn+2) 1 2n +3 3. Е 'n* +3п + 2 4.…

A: 1,2,4 Convergent series 3,5 Divergent series

Q: Q8) The sequence 5 +(-1)" an' a) converges to 1 b) converges to c) converges to 0 d) diverges |5

A: an = 5+(-1)n5      = ∑n=1∞5+(-1)n5 =∞ ∑n=1∞5+(-1)n5 diverges to ∞

Q: Which of the following is true about the sequence In (3n² − n² + 1) − ln(n³ + 2n¹ + 5n)? = an The…

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Q: (3) Find all p ER so that 3n² + 2n +1 n2p-1 + 137 n=1 converges. As always, your answer must be…

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Q: 6n The sequence a, 20 +64n 3. OA Converges to 4 13 OB. Converges to 32 OC. diverges O D.None of…

A: We will solve the following.

Q: If C.)" converges, then C,)" converges. n=0 n=0 Select one: True False

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Q: Š V2n-5 n=1 n2- 3n +4

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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: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: 8. 5n The sequence 1+ 5n n=1 Converges to Ve O None 1 Converges to 1. Converges to Ve Diverges

A: We have to solve

Q: n! The sequence converges to 0 (100)6n Select one: O True O False

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Q: If Ea, converges , then n=1a, diverges n=1 an n=1 Select one: O True O False

A: given sequence are, given that 1st sequence is converges and we have to find 2nd sequence is…

Q: Question 15 -(#)" n 11 State whether the sequence ɑn = converges and, if it does, find the limit. а)…

A: Given sequence is an=11nn

Q: 2 – 5n 11п-1 n=1

A: Use ratio test.

Q: Suppose that the sequence (c,) converges to -1. Which of the following sequences converges to 2…

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Q: If k-P converges, then k-p+0.001 converges. k=1 k=1

A: If ∑k=1∞k-p converges, then ∑k=1∞k-p+0.001 converges.

Q: 22n Σ n! n=1

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Q: 1. Determine if the following sequences are convergent or divergent. Show all steps. a) an = (-1)n…

A: SOLUTION-

Q: If 2 an converges for some large k, then so will ) n=k n=1 Select one: O True 17 O False

A: It can be solved using the simple observation.

Q: PART III: Decide whether each of the following converges absolutely or con- ditionally. Justify your…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: The sequence 7² – 1 - V n² +n converges to – 2 Select one: 23 True O False

A:

Q: 11. You find that the recursion relation is given by 2n + 1 an n + 2 An+3 What is the radius of…

A: Consider the provided question, The recursion relation is given by, an+3=2n+1n+2an

Q: (-1)** 3³3n Зп Use the root test to determine if > converges or diverges. 52n+3 n=1

A: Given series is

Q: 1 'n² – n-6 n=4

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Q: n2 3" 1) > 6n+1 n=1

A: Given query is to find the series converging or diverging.

Q: If > an converges, then a converges. n=1 n=1

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Q: The largest whole number k for which 2k (ke") 52n+3 (kn² + 5) n=1 converges is .....

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Q: + inf 1 Σ п2 — Зп + 2 n=3 W

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Q: 1 The sequence converges to ,? – 1 – V n² +n | Select one: True 21 False

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Q: the sequence converges or diverges. {an} = {: 5n5 + 8n³ – 12 } %3D n3 +3n2 -7n + 8

A:

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: 3n-1 Investigate if the following sequence converge or diverge = 0 10n4S? 00 %3D

A: So to find that series is convergent or divergent, Ratio method has been used.

Q: an converges for some large k, then so will n=1 an- If E n=k

A: We have to check

Q: Determine if the two given converges or diverges. { п n 2n + - 1/ n=1 Σ n n \2n + 1 n=1

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Q: O Does Eo 2k+² e-k converge or diverge? If it converges find the sum. "k=1'

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Q: Question E. Use the Squeeze Theorem and Corollary 1.1 to prove that the sequence converges to 0. 1…

A: To prove the convergence using Squeeze theorem.

Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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Q: the series : 2 3 3 5 Select one: a. converges absolutely O b. converges conditionally c. diverges d.…

A: Check the given series by limit comparision test.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.