4. Discuss the convergen (a) 2"e-n.

Q: Which of the followings are true? 1.En=1 7?+Inn (-1)" is absolutely convergent. II. >n=1 (-1)m is…

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Q: 1 10. Determine by the root test if Ln=1 converges or diverges. (In(n+1))“

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Q: 2. n=2 nlogn does not converge but En-2 nlog²n converges. Show that Z2 [Hint: you might find it…

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Q: 5. Determine if Σn=3 convergent. cos(NT) is absolutely convergent or conditionally n+1

A: "Absolute convergence" means a series will converge even when you take the absolute value of each…

Q: 1. Which sequence converges? 3 (А) а, 3 п+- (-1)" sin 2 (A) (B) a, = -1+- (C) a, = п n! (D) а, 3D 3"…

A: Sequence

Q: Rigorously show that (-1)"-1. n2 +1 is conditionally convergent. n=1

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Q: Which of the followings are true? 1. E is absolutely convergent. 00 n=1 n! II. En-1 (-1)-1 is…

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Q: Which of the followings are false? 1. E (-1)" Ln-1 n+ Inn is absolutely convergent. 2n (-1)* 2…

A: We have to choose the correct answer

Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

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Q: 2 then E " Cn+1 converges. 3.11 limnr+m

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Q: For each positive integer k, let H, (k) be the smallest harmonic number larger than k and define the…

A: As per the question we have to check that wheather the given sequence E(k) is convergent or not.

Q: QUESTION 14 14. Which of the following sequences is/are convergent? (-) n I. an = 4n2 II. an n² + 3…

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Q: Which of the followings are true? (-1)" 1. En-1 n²+Inn is absolutely convergent. (-1)* II. En-1 is…

A: We have to find the option

Q: Which of the followings are false? 1. E0 (-1)* m%=D1 2+irn is absolutely convergent. (-1)2. is…

A: which of the following is false

Q: (- 1)"+(- =D1 converges conditionally in elect one: True

A: Please refer to the image below

Q: 1. One of the following sequences is divergent 1 (A) an 72 (B) S, = k=1 (-1)" (C) cn = 2n3 (D) b, =…

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Q: Match each of the following with the correct statement. C stands for Convergent, D stands for…

A: Concept used: Divergence: When the values goes to -∞ or goes to ∞ that is it does not approach one…

Q: Which of the followings are true? 1.En 1 nInn (-1)" is absolutely convergent. 11. En 1 (-1) is…

A: Option (e) is correct.

Q: 3. Show that if X and Y are sequences such that X and X + Y are convergent, then Y is convergent.

A: Given, sequences  and  such that  and  is convergent.It is required to prove that  is…

Q: Which of the followings are true? 2" n1 n! 1. E is absolutely convergent. II. E 1 (-1)"-1 is…

A: see second step

Q: 3.2.6 Theorem If X (x) then a < lim(x) b. is a convergent sequence and if a S X5bfor all n e N,

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Q: Σ (-1)* converges. Vk Determine whether k=1

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Q: Which of the followings are false? is absolutely convergent. 1. Ln=1 (-1)*-1 is absolutely…

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Q: 2. (a) Write the first 5 terms of the sequences with general terms an below and indicate whether…

A: As per the guidelines, we are suppose to answer only the first 3 subparts.  Repost the rest of the…

Q: 16.) Given a, >0 for all k and given a, is convergent, then which one of the following must also k-1…

A: Q. 16 Given ak&gt;0 for all k and the series ∑k=1∞ak is convergent. Which means ∑k=1∞ak = Some…

Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

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Q: Sn/2", l1/2". if n is a prime number otherwise. Let an Does Ea, converge? Give reasons for your…

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Q: 2. Give examples (without proofs) of the following: a) sequences {xn} and {yn} which both diverge,…

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