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2. Define a sequence (a) by a=1, an+1 dn Vn E N. (n + 1)2 Does the sequence converge? Find the limit if it does. n+1 Hint: Write a few terms of the sequence explicitly and try to see by patterns that in fact, a, = be established rigorously. This of course needs to 2n

2. Define a sequence (a) by a=1, an+1 dn Vn E N. (n + 1)2 Does the sequence converge? Find the limit if it does. n+1 Hint: Write a few terms of the sequence explicitly and try to see by patterns that in fact, a, = be established rigorously. This of course needs to 2n

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. Define a sequence (a,) by a = 1, an+1 = an Vn E N. (n+ 1)2 Does the sequenece converge? Find the limit if it does. n+1 Hint: Write a few terms of the sequence explicitly and try to see by patterns that in fact, an be established rigorously. This of course needs to 2n
Transcribed Image Text:2. Define a sequence (a,) by a = 1, an+1 = an Vn E N. (n+ 1)2 Does the sequenece converge? Find the limit if it does. n+1 Hint: Write a few terms of the sequence explicitly and try to see by patterns that in fact, an be established rigorously. This of course needs to 2n
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