ch of the following statements are correct for n2+1, n4+1 n² n=0 I) converges by the nth term test. II) converges by the limit comparison test with comparison n2 n=1

Q: Which of the following statements best justifies In(n+ 1)

A: We are given the following series.               We know that ln(x) < x. So, ln(n+1)/n will…

Q: Use the limit comparison test 5. 8n +7 In n- 2 n=1 O Converges O Diverges

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

Q: Consider the sequence P,3D0.3)4" the the order and the asymptotic error constant when the sequence…

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Q: k2 +k Use the limit comparison test to determine whether kA+2 converges.

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Q: Which of the following assertions is true for the given sequences? a) {(-1)" e"} converges п+1 b)…

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :…

Q: Show theit the fenias +- (AtI)(28+1) (P+1)(2p41)(38+1) (uhese a>0, B>0) conveages if B>a amd…

A: Ratio test If we have series ∑ann=1∞ Then we will find the limit l = limn→∞an+1an If l<1 , then…

Q: Use the comparison test to determine whether) converges. 2 +3* k-1

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Q: Diff eqn. 25) y' + (tan x)y = cos x when -pi/2 < x < pi/2

A: NOTE: Refresh your page if you can't see any equations. . compare this DE with  so here we have

Q: n - 3 п - 3 1 (-1)" converges absolutely because 0 3. Зп + 1 Зп + 1 n=1

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Q: 7

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Q: What are all of the values of x ,such that (-1)*+(n) * converges? (). x1.40

A: Using ratio test a series converges iff:…

Q: Determine if the sequence converges or diverges. Briefly justify! When she converges provide her…

A: find the limit of given sequence at infinity.

Q: What are all of the values of x ,such that - (-1) n+A converges? n=1 .1 X26 .2 06

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Q: Test for fallowing convergences. of h= 1

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

Q: True or false: if (n) converges, then every subsequence (n) is Cauchy. Select one: O True O False

A: True or false

Q: (Q2) Prove directly from the definition that the following sequence converges. 8n²+(-5) n

A: The given sequence is 8n2+-5n5n2+n+-1nn∈ℕ* The objective is to prove that this sequence converges…

Q: Q3) The sequence a, = 1 - (0.2)" a) converges to 0 b) diverges c) converges to e d) converges to 1

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Q: 1. Prove that the sequence {4+} converges to 4.

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: 4. Use the basic comparison test (not the limit comparison test, or any other test) 00 Σ To show…

A: Given series : ∑n=0∞55n+5

Q: 1 3. Use the Limit Comparison Test to determine whether converges or diverges. Vnvn+1 n=1

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Q: converges? What are all of the values of x such that x1.20 >0.3 x<0.40

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Q: 9. Use the definition of convergence to prove that the sequence converges. b) {2n/(3n + 2)} c)…

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Q: Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ²).…

A: Given equality: ∑i=0nxi·∑i=0nyi=∑i=0nxiyi   a) Verify the equality is always true. If not, give an…

Q: Given that " In (1) converges, does [.. converge or diverge? In(n) 1 (²+5)² A. Diverges B. Cannot be…

A: Let ∑pn and ∑qn are two series such that pn≤qn. If ∑qn is convergent, then ∑pn is convergent.

Q: 10a) Consider the following sequence of numbers defined recursively: a, = 3, a, = V3, az = V3 + v3.…

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Q: an 57" n! nal

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Q: Hi, can you tell me if the following is true or false?

A: First statement is false because

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.