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Let (an) be a sequence of real numbers and let a € R. Which of the following statements are equivalent to "aaasn→∞"? You should select THREE answers. □ a. N:n> N⇒a € a-e₁a+e]. O b. Let b₁ = ax an. Then ba² as n → ∞0. c. 30, NEN:n> N⇒a € (a − ‹‚a + €). N⇒ ₂ − a < e. Od. Ve > 0,3NEN:n> □e. Ve > 0,3N EN:n>N⇒a₂ € (a-e,a+€).

Let (an) be a sequence of real numbers and let a € R. Which of the following statements are equivalent to "aaasn→∞"? You should select THREE answers. □ a. N:n> N⇒a € a-e₁a+e]. O b. Let b₁ = ax an. Then ba² as n → ∞0. c. 30, NEN:n> N⇒a € (a − ‹‚a + €). N⇒ ₂ − a < e. Od. Ve > 0,3NEN:n> □e. Ve > 0,3N EN:n>N⇒a₂ € (a-e,a+€).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let (an) be a sequence of real numbers and let a E R. Which of the following statements are equivalent to "aa as n → ∞o"? You should select THREE answers. a. 0,3N:n> N⇒ a € [a-e,a+el. b. Let bn = ax an. Then ba² as n → ∞o. c. 3 > 0,3 EN:n> N⇒ a € (a-e, a + €). Od. Ve > 0,3N EN:n > N⇒la - a| < e. □e. Ve > 0, EN EN:n>N⇒a € (a-e, a + €).
Transcribed Image Text:Let (an) be a sequence of real numbers and let a E R. Which of the following statements are equivalent to "aa as n → ∞o"? You should select THREE answers. a. 0,3N:n> N⇒ a € [a-e,a+el. b. Let bn = ax an. Then ba² as n → ∞o. c. 3 > 0,3 EN:n> N⇒ a € (a-e, a + €). Od. Ve > 0,3N EN:n > N⇒la - a| < e. □e. Ve > 0, EN EN:n>N⇒a € (a-e, a + €).
Expert Solution
Step 1

Let an be sequence of real numbers and let a∈ℝ.

We have given that limn→∞an=a.

We need to identify which of the given statements are correct.

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