1).  State whether the statement is true, or give an example to show that it is false. If ∞     n = 1anxn converges, then anxn → 0 as n → ∞. i).  True

Q: 3. Use the Test for Divergence to explain why if En-0 an converges, then En=0 am must diverge.

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Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

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Q: Help for 2a,2b,2c.

A: Given,

Q: 1+ 1 + 1 V 3 + 1 43 Select one: Qa converges O b. It is inconclusive O c. diverges +...

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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: Exercise 2.1.6: Is the sequence{; Exercise 2.1.7: Let {xn} be a sequence. a) Show that lim xn = 0…

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Q: b) Suppose (xn) does not converge to 0. Then there exists e > 0 such that all except for finitely…

A: Let us suppose the following sequence xn=1,0,1,0,1,0,..... We have to see that the odd terms are 1…

Q: For eksample Xn = n² (n+1)! investigate whether the serles Σ 8 n=1 Xn convergent Or divergent. Prove…

A: We will use ratio test to check whether given series is convergent or not.

Q: Suppose (xn) does not converge to 0. Then there exists e>0 such that all except for finitely many…

A: Consider the sequence xn=1,0,1,0,1,0,....... Here the odd terms are 1 and the even terms are 0.…

Q: 9. Prove that if {fn(x)} converges uniformly to the function f(x) on each of the sets A1, A2, ...,…

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Q: Exercise 4. 1. Show that if (fn)n converges uniformly on S, then (fn)n converges uniformly on every…

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Q: Suppose (an) is a sequence of positive real numbers such that an+1 Prove that liman (an) even…

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Q: ,(-1)" converges conditionally, but not absolutely. Show all work. 3n Prove E

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Q: 3η 9.) Ž(-1 2η 9.) Σ n=1

A: Given: ∑n=1∞2nn-13n To Determine: Series is Convergent or Divergent Concept: Root Test:If we have…

Q: Show that a, converges to A iff {a, - A) converges to 0.

A: Answer

Q: 2.65 Let fn(x) = xe¬nx² a) Find || fn||sup for all n. b) Determine whether or not fn converges…

A: The given function is fn(x)=xe-nx2 ∀x∈ℝ To find: (a) ∥fn(x)∥Sup ∀n             (b) Whether…

Q: If Ea, converges absolutely, prove that Ea,² converges.

A: