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Let S = Σan be a series. n=0 Which of the following statements must be true? Select all the correct answers. IF lim an = 0, THEN the series S is CONVERGENT. 0042 IF the series S is DIVERGENT, THEN lim an = 0. n→∞ = 0. IF the series S is CONVERGENT, THEN_liman = 0042 IF an is DIVERGENT, THEN lim an 0. n→∞ n=1 IF n=1 an is DIVERGENT, THEN Σ an = ∞0 n=1 IF lim an ‡0, THEN the series S is DIVERGENT. n→∞

Let S = Σan be a series. n=0 Which of the following statements must be true? Select all the correct answers. IF lim an = 0, THEN the series S is CONVERGENT. 0042 IF the series S is DIVERGENT, THEN lim an = 0. n→∞ = 0. IF the series S is CONVERGENT, THEN_liman = 0042 IF an is DIVERGENT, THEN lim an 0. n→∞ n=1 IF n=1 an is DIVERGENT, THEN Σ an = ∞0 n=1 IF lim an ‡0, THEN the series S is DIVERGENT. n→∞

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 S = Σan be a series. n=0 Which of the following statements must be true? Select all the correct answers. IF lim an = 0, THEN the series S is CONVERGENT. 0042 IF the series S is DIVERGENT, THEN lim an = 0. n→∞ = 0. IF the series S is CONVERGENT, THEN_liman = 0042 IF an is DIVERGENT, THEN lim an 0. n→∞ n=1 IF n=1 an is DIVERGENT, THEN Σ an = ∞0 n=1 IF lim an ‡0, THEN the series S is DIVERGENT. n→∞
Transcribed Image Text:Let S = Σan be a series. n=0 Which of the following statements must be true? Select all the correct answers. IF lim an = 0, THEN the series S is CONVERGENT. 0042 IF the series S is DIVERGENT, THEN lim an = 0. n→∞ = 0. IF the series S is CONVERGENT, THEN_liman = 0042 IF an is DIVERGENT, THEN lim an 0. n→∞ n=1 IF n=1 an is DIVERGENT, THEN Σ an = ∞0 n=1 IF lim an ‡0, THEN the series S is DIVERGENT. n→∞
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