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Which of the following statements are true? I. lim Vn2 sin(n?) = 1. n+1 II. Let {an} be a convergent sequence of real a1 +.. + an numbers. If ba then the sequence {bn} is also convergent and lim bn = lim an. n 00 III. lim arctan n = 0. 4n IV. Lemma: For any sequence {an} of real numbers, lim azk lim azk+1 = L if and only if %3D lim an = L; (LE R). By the lemma above, one can obtain that (-1)"-n if an = - -- + n 4. + - n - - 1 then lim an %3D 2 n00 I, III III, IV (a) (b) II, IV I, II, III II, III, IV (c) (d) (e)

Which of the following statements are true? I. lim Vn2 sin(n?) = 1. n+1 II. Let {an} be a convergent sequence of real a1 +.. + an numbers. If ba then the sequence {bn} is also convergent and lim bn = lim an. n 00 III. lim arctan n = 0. 4n IV. Lemma: For any sequence {an} of real numbers, lim azk lim azk+1 = L if and only if %3D lim an = L; (LE R). By the lemma above, one can obtain that (-1)"-n if an = - -- + n 4. + - n - - 1 then lim an %3D 2 n00 I, III III, IV (a) (b) II, IV I, II, III II, III, IV (c) (d) (e)

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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Which of the following statements are true? Vn² sin(n²) lim I. = 1. n +1 II. Let {an} be a convergent sequence of real a1 +. + an numbers. If bn then the sequence {bn} is also convergent and lim bn lim an- arctan n III. lim 0. 4n IV. Lemma: For any sequence {an} of real numbers, lim a2k = lim a2k+1 = L if and only if lim an = L; (L ER). n+00 By the lemma above, one can obtain that 1 (-1)"-1n = - - - + - if an 4 - - + n 1 then lim Jan| (a) I, III (b) III, IV П, IV (d) I, II, III (c) (e) II, III, IV
Transcribed Image Text:Which of the following statements are true? Vn² sin(n²) lim I. = 1. n +1 II. Let {an} be a convergent sequence of real a1 +. + an numbers. If bn then the sequence {bn} is also convergent and lim bn lim an- arctan n III. lim 0. 4n IV. Lemma: For any sequence {an} of real numbers, lim a2k = lim a2k+1 = L if and only if lim an = L; (L ER). n+00 By the lemma above, one can obtain that 1 (-1)"-1n = - - - + - if an 4 - - + n 1 then lim Jan| (a) I, III (b) III, IV П, IV (d) I, II, III (c) (e) II, III, IV
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