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

Q: Q3. Assuming that e = 2.71828182845... is correct to 11 decimal places, show that is a convergent to…

A: Convergent rational number

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

A: The given series is

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: 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: 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: Let a > 0. Show that the series E(1+ a")-1 is divergent if 0 1

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Q: 1 'n² – n-6 n=4

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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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