Prove from first principles (i.e. give a direct e-N proof) that the following se- quence converges: an 3n + 1 2n-1

Q: K+1 – /K k=1 VK² - +K

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Q: 00 Show that converges if [r| < 1. п: п

A: The given series is

Q: et r ER. Find all r for which [(n≥2) 1/ (n (logn)^r)) converges.

A: Series is a combination of the term of the sequence. The convergent series is defined as convergent…

Q: D) { (-)"} [Select] [Select] converges to 2.

A: Please see the below picture for detailed solution.

Q: H.w.Which af the fallowing series converge or diverg 80 Ln n 2. (h+i)! hai 4- n+4

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Q: What is the value of p = lim+¹ when applying the Ratio Test to assess n→∞an a convergence of? What…

A: Given problem:-

Q: Given: a, = In(n + 1) – In(n) for n E N || Determine if the following is convergent or divergent.…

A: Given  an = lnn+1 - lnn for n∈ℕ.

Q: Exercise 8. Discuss the uniform convergence of the following series. sin(nx) [0, 27). on

A: (8) Consider the provided question, Given series,  ∑sinnxn  on 0, 2π We need to discuss the uniform…

Q: Exercise 8. Discuss the uniform convergence of the following series. sin(nx) Σ on (0, 27). on R. cos

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Q: Are the following convergent or divergent? Show your work and state the reason 100 11) Ση n=0

A: The summation of n, n from 0 to 100.

Q: Show that if a&gt;-1 and b&gt;a+1 , then the followingintegral is convergent.

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Q: 1. (a) Let an → 2. Prove from first principles (i.e. give a direct e-N proof) that a → 4. (b) Let a?…

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Q: The series 00 1 + Vn? 1 + Vna n=1 is convergent if and only if: Select one: Oa. 72 a > Ob. 35 a 4…

A: (.)   The given series is ,                                                        ∑n=1∞1+n281+na7…

Q: 3. Let for n € N. Is convergent? a₁ = 1, an+1 Σ n=1 = An sin an

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Q: b. Eel/n – el/n+1 n=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: Let a > 0. Show that the series E(1+ a")-1 is divergent if 0 1

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Q: 1.The series E-1)" 00 converges lor all x.

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Q: 1 'n² – n-6 n=4

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Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to

A: We have to solve

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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Q: ca, is convergent. is an convergent and c is a nonzero constant, then If n=1 n=1

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Q: 1 Prove: Ex-1 n=1 (n+1)(log(n+1)), converges for p > 1 and diverges for p ≤ 1.

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Q: 1. Prove that the series E(-1)" n converges uniformly in any closed and bounded interval a, b, but…

A: 1st we prove the uniform convergence part

Q: Determine whether the sum ∞ n=1 (In(n)) ¹2 n9/8 converges or diverges, and explain why.

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Q: Use the Ratio Test to determine whether the series (-1)"- n! is convergent. n=1

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Q: finding if this converges or diverges

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