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(a) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 > can is also divergent. n=1 (b) Let sn = a1 + ... + an. If lim sn =0, then the series ) an is convergent. n=1 (c) Given the alternating series (-1)"an. If an is increasing or lim an #0 then the n=1 given series is divergent. I. Determine whether the following sequence is convergent or divergent. Justify your answer. {Vñ- Vn+1}

(a) Suppose the infinite series an is divergent. Then for any constant c, the series n=1 > can is also divergent. n=1 (b) Let sn = a1 + ... + an. If lim sn =0, then the series ) an is convergent. n=1 (c) Given the alternating series (-1)"an. If an is increasing or lim an #0 then the n=1 given series is divergent. I. Determine whether the following sequence is convergent or divergent. Justify your answer. {Vñ- Vn+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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I. Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) Suppose the infinite series ) an is divergent. Then for any constant c, the series n=1 8. > can is also divergent. n=1 (b) Let sn = a1 + ... + an: If lim sn = 0, then the series )` An is convergent. n=1 (c) Given the alternating series (-1)"an. If an is increasing or lim an #0 then the n=1 given series is divergent. II. Determine whether the following sequence is convergent or divergent. Justify your answer. {Vn- Vn+1} III. For each of the following series, determine whether it is convergent or divergent. Justify your answer briefly (1-2 sentences ONLY). +oo +00 (п — 1)2 n2 + 1 -5 ( a) Σ (n +2)² (c) > un where sn = u1+...+un = n=3 n=1 (b) - n 72-n n=1 IV. Determine whether the given series is convergent or divergent. Justify your answers. (c) E(-1)"_(2n)! 2(n + 1) +o0 1 (a) Σ 16n2 + 8n – 3 n=1 n=1 In n (b) E(-1)"- n2 n=2 (-1)"3næ" n² – 5 V. Determine the interval of convergence of > n=1 VI. Give the Maclaurin series expansion of f(x) convergence. Approximate In(0.5) using the first 5 terms using the expansion. In(2 – 3x). Determine its interval of %3D
Transcribed Image Text:I. Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) Suppose the infinite series ) an is divergent. Then for any constant c, the series n=1 8. > can is also divergent. n=1 (b) Let sn = a1 + ... + an: If lim sn = 0, then the series )` An is convergent. n=1 (c) Given the alternating series (-1)"an. If an is increasing or lim an #0 then the n=1 given series is divergent. II. Determine whether the following sequence is convergent or divergent. Justify your answer. {Vn- Vn+1} III. For each of the following series, determine whether it is convergent or divergent. Justify your answer briefly (1-2 sentences ONLY). +oo +00 (п — 1)2 n2 + 1 -5 ( a) Σ (n +2)² (c) > un where sn = u1+...+un = n=3 n=1 (b) - n 72-n n=1 IV. Determine whether the given series is convergent or divergent. Justify your answers. (c) E(-1)"_(2n)! 2(n + 1) +o0 1 (a) Σ 16n2 + 8n – 3 n=1 n=1 In n (b) E(-1)"- n2 n=2 (-1)"3næ" n² – 5 V. Determine the interval of convergence of > n=1 VI. Give the Maclaurin series expansion of f(x) convergence. Approximate In(0.5) using the first 5 terms using the expansion. In(2 – 3x). Determine its interval of %3D
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