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Answer and give a brief (1-2 sentence) explanation for each of the following questions. (a) Suppose we know that lim S, = 3, where S, = > `an is the nth partial sum of the series An. n 00 n=1 i. Do we know for sure whether an converges? If the answer is yes, determine the sum (if n=1 possible). ii. Determine lim an (if possible). (b) Suppose instead we only know that lim an = 3. Do we know for sure whether > `an converges? n=1 If the answer is yes, determine the sum (if possible). (c) Finally, suppose the only information we have is that lim an = 0. Do we know for sure whether n 00 Σ an converges? If the answer is yes, determine the sum (if possible). n=1

Answer and give a brief (1-2 sentence) explanation for each of the following questions. (a) Suppose we know that lim S, = 3, where S, = > `an is the nth partial sum of the series An. n 00 n=1 i. Do we know for sure whether an converges? If the answer is yes, determine the sum (if n=1 possible). ii. Determine lim an (if possible). (b) Suppose instead we only know that lim an = 3. Do we know for sure whether > `an converges? n=1 If the answer is yes, determine the sum (if possible). (c) Finally, suppose the only information we have is that lim an = 0. Do we know for sure whether n 00 Σ an converges? If the answer is yes, determine the sum (if possible). n=1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Answer and give a brief (1-2 sentence) explanation for each of the following questions. n (a) Suppose we know that lim S, 3, where Sn =) `an is the nth partial sum of the series An. n→∞ i=1 n=1 i. Do we know for sure whether > an converges? If the answer is yes, determine the sum (if n=1 possible). ii. Determine lim an (if possible). (b) Suppose instead we only know that lim an = 3. Do we know for sure whether). An converges? n→∞ n=1 If the answer is yes, determine the sum (if possible). (c) Finally, suppose the only information we have is that lim an = 0. Do we know for sure whether Σ An converges? If the answer is yes, determine the sum (if possible). n=1
Transcribed Image Text:Answer and give a brief (1-2 sentence) explanation for each of the following questions. n (a) Suppose we know that lim S, 3, where Sn =) `an is the nth partial sum of the series An. n→∞ i=1 n=1 i. Do we know for sure whether > an converges? If the answer is yes, determine the sum (if n=1 possible). ii. Determine lim an (if possible). (b) Suppose instead we only know that lim an = 3. Do we know for sure whether). An converges? n→∞ n=1 If the answer is yes, determine the sum (if possible). (c) Finally, suppose the only information we have is that lim an = 0. Do we know for sure whether Σ An converges? If the answer is yes, determine the sum (if possible). n=1
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