1. Use the Monotone Convergence Theorem to show that the following sequence 1.3-5.(2n – 1) 2.4.6(2n) Sn n=1 is convergent. 2. Determine if the series given by +00 (In(n) Σ n" n=1 is convergent or divergent.

Q: 3. n-3n+5 n7 Sn=1

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Q: (1) Suppose that (an) tends to infinity. (a) Suppose that (bn) tends to minus infinity. What can you…

A: Let's delve into a detailed step-by-step explanation: (a) Sequence ( (anbn) ) as ( n ) goes to…

Q: 9. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

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Q: th (a) Prove that the sequence with n' (b) Prove that (sn) does not converge to 1. term Sn - does…

A: We know, that if two convergent sequences they converging to s and t respectively and  for all n…

Q: Exercise 0.5. Study the convergence of the series (1) Lnz2 [n+(-1)"|²

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Q: 3. Give an example of divergent series n=1dn and Ln=1 6n for which the series ("q + "p) converges.

A: Given: that An example of divergent series ∑n=1∞ an and ∑n=1∞ bn for which the series  ∑n=1∞ an+bn…

Q: Determine which of the following infinite series converge: Inn (a) (15 points) Σn-1 n (2n + 1) (2n −…

A: To determine whether the series ∑n=1∞​n(2n+1)(2n−1)lnn​ converges or diverges, we can analyze its…

Q: Find the partial sum Sn of the sequence an=log(n+5/n+6)

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Q: Show whether each of the following series and sequences converges or diverges. If convergent, enter…

A: Divergent test : If limk→∞ ak ≠0 then ∑k=1∞ ak is divergent .

Q: Find the interval of convergence for the given infinite geometric series. 6+ 6 (x + 3) + 6 (x + 3)²…

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Q: 1. Prove that the sequence converges to . 2n+1

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Q: how that the sequence (1 – (-1)" +1/n) is divergen

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Q: n-1 (a) n+1 Converges or Diverges: limit (If Converges): (b) Ž"-1 n=1 N+1 Converges or Diverges:…

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