2" 1 and b, = en 1 for n > 1. 1. Let an = 100 + (п +3)! en+1 1201 (a) Show that {an}1 is monotone, and is bounded below and above by 100 and respectively 12 (b) Use (a) to conclude that {an}=1 converges to a nonzero limit. (Hint: If {a,} is convergent and a, > M for all n, then lim a, > M.) (c) Determine whether bn is convergent or divergent. If the series is convergent, find its sum. n=1
2" 1 and b, = en 1 for n > 1. 1. Let an = 100 + (п +3)! en+1 1201 (a) Show that {an}1 is monotone, and is bounded below and above by 100 and respectively 12 (b) Use (a) to conclude that {an}=1 converges to a nonzero limit. (Hint: If {a,} is convergent and a, > M for all n, then lim a, > M.) (c) Determine whether bn is convergent or divergent. If the series is convergent, find its sum. n=1
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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Transcribed Image Text:2n
1
and bn =
en
1
for n > 1.
1. Let an = 100+
(п + 3)!
en+1
1201
(a) Show that {an}=1 is monotone, and is bounded below and above by 100 and
respectively.
12
(b) Use (a) to conclude that {a,}1 converges to a nonzero limit.
(Hint: If {a,} is convergent and a, > M for all n, then lim a, > M.)
(c) Determine whether > b, 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
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