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2" Let an = 100+ and bn 1 for n >1. (n +3)! en en+1 (a) Show that {am} is monotone and bounded below and above by 100 and 1201 -, respectively. 12 (b) Prove that {an}=1 converges, but NOT to 0. (c) Determine whether bn is convergent or divergent. If the series is convergent, find its sum. n=1

2" Let an = 100+ and bn 1 for n >1. (n +3)! en en+1 (a) Show that {am} is monotone and bounded below and above by 100 and 1201 -, respectively. 12 (b) Prove that {an}=1 converges, but NOT to 0. (c) Determine whether bn is convergent or divergent. If the series is convergent, find its sum. n=1

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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2" 1 and bn en 1 for n >1. Let an 100 + (n + 3)! en+ï (a) Show that {an}=1 is monotone and bounded below and above by 100 and 1201 , respectively. 12 (b) Prove that {an}=1 converges, but NOT to 0. (c) Determine whether bn is convergent or divergent. If the series is convergent, find its sum. n=1 (d) Determine whether > (an + bn) is convergent or divergent. n=1 Determine the convergence or divergence of the following series. 1 (a) E (Use Integral Test.) n(ln n)4 n=2 (b) Σ cos? n + n!/3 n=1
Transcribed Image Text:2" 1 and bn en 1 for n >1. Let an 100 + (n + 3)! en+ï (a) Show that {an}=1 is monotone and bounded below and above by 100 and 1201 , respectively. 12 (b) Prove that {an}=1 converges, but NOT to 0. (c) Determine whether bn is convergent or divergent. If the series is convergent, find its sum. n=1 (d) Determine whether > (an + bn) is convergent or divergent. n=1 Determine the convergence or divergence of the following series. 1 (a) E (Use Integral Test.) n(ln n)4 n=2 (b) Σ cos? n + n!/3 n=1
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