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58) Which of the following statements are true? a) The integral dx converges. b) The seriesE)" converges. n=1 c) The series (In(n))In(n) COnverges. n=5 d) The integral Tntel dx converges. (In(z))ln(=) (In(n))In(In(r)) n=5

58) Which of the following statements are true? a) The integral dx converges. b) The seriesE)" converges. n=1 c) The series (In(n))In(n) COnverges. n=5 d) The integral Tntel dx converges. (In(z))ln(=) (In(n))In(In(r)) n=5

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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Solve both 58 and 59 please

58) Which of the following statements are true? a) The integral dx converges. b) The series E)" converges. n=1 c) The series Tnim converges. (In(n))In(7) n=5 d) The integral Intala dx converges. (In(r))ln(=) e) The series E (In(n))In(In(n)) (In(n)) Converges. n=
Transcribed Image Text:58) Which of the following statements are true? a) The integral dx converges. b) The series E)" converges. n=1 c) The series Tnim converges. (In(n))In(7) n=5 d) The integral Intala dx converges. (In(r))ln(=) e) The series E (In(n))In(In(n)) (In(n)) Converges. n=
59) Assume that an > 0 for all n e N and an+1 < an for all n > 100. Consider the series an n=1 k with k-th partial sum Sk = E(-1)"+1an. n=1 Which of the following statements are true? a) The series converges if and only if lim an = 0. = 0. n00 b) If E(-1)"+'a, converges to S, then S12 < S < S13. n=1 c) If E(-1)"+l an converges to S, then S234 < S < S235. n=1 d) If E(-1)"+an converges to S, then |S – S45| < a46- n=1 e) If E(-1)"+'am converges to S, then |S – S239| < a240- n=1
Transcribed Image Text:59) Assume that an > 0 for all n e N and an+1 < an for all n > 100. Consider the series an n=1 k with k-th partial sum Sk = E(-1)"+1an. n=1 Which of the following statements are true? a) The series converges if and only if lim an = 0. = 0. n00 b) If E(-1)"+'a, converges to S, then S12 < S < S13. n=1 c) If E(-1)"+l an converges to S, then S234 < S < S235. n=1 d) If E(-1)"+an converges to S, then |S – S45| < a46- n=1 e) If E(-1)"+'am converges to S, then |S – S239| < a240- n=1
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