Define a sequence {a„}, by An+1 ɑj = 10. An First, note that a, > 0 for all n. Answer the following questions. (a) Explain why an 2 /2 for all n. (b) Explain why {a„}1 is non-increasing (that is, monotonically decreasing). (c) Explain why the limit lim a„ exists, and find the limit.
Define a sequence {a„}, by An+1 ɑj = 10. An First, note that a, > 0 for all n. Answer the following questions. (a) Explain why an 2 /2 for all n. (b) Explain why {a„}1 is non-increasing (that is, monotonically decreasing). (c) Explain why the limit lim a„ exists, and find the limit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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2.
Define a sequence {a,}1 by
-{(--2).
An+1
ɑj = 10.
an
First, note that a, > 0 for all n. Answer the following questions.
(a) Explain why a, 2 /2 for all n.
(b) Explain why {an}1 is non-increasing (that is, monotonically decreasing).
(c) Explain why the limit lim a, exists, and find the limit.
112"
Transcribed Image Text:%24
2.
Define a sequence {a,}1 by
-{(--2).
An+1
ɑj = 10.
an
First, note that a, > 0 for all n. Answer the following questions.
(a) Explain why a, 2 /2 for all n.
(b) Explain why {an}1 is non-increasing (that is, monotonically decreasing).
(c) Explain why the limit lim a, exists, and find the limit.
112
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