Which of the following statements are true? ³n² sin(n²) I. lim : 1. n→∞0 n+1 II. Let {an} be a convergent sequence of real a₁ + ... + an numbers. If b = then n the sequence {n} is also convergent and lim b= lim an. n-x n-x arctan n III. lim 0. n-x 4n IV. Lemma: For any sequence {an} of real numbers, lim a2k = lim a2k+1 = L if and only if k→∞ k→∞ lim an = L; (LER). 14x By the lemma above, one can obtain that 1 2 (−1)n-1n if an + n n then lim an = 14x (a) I, III (b) III, IV (c) II, IV (d) - I, II, III (e) II, III, IV SIN n + 48 315 112 n n
Which of the following statements are true? ³n² sin(n²) I. lim : 1. n→∞0 n+1 II. Let {an} be a convergent sequence of real a₁ + ... + an numbers. If b = then n the sequence {n} is also convergent and lim b= lim an. n-x n-x arctan n III. lim 0. n-x 4n IV. Lemma: For any sequence {an} of real numbers, lim a2k = lim a2k+1 = L if and only if k→∞ k→∞ lim an = L; (LER). 14x By the lemma above, one can obtain that 1 2 (−1)n-1n if an + n n then lim an = 14x (a) I, III (b) III, IV (c) II, IV (d) - I, II, III (e) II, III, IV SIN n + 48 315 112 n n
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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