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(5) Consider the sequence defined by S1 = 1 Sn+1 = (sn +2) for n > 1 (a) Prove by induction 0 Sn <1 for all n E N (b) Prove the sequence is monotone. (c) Use the previous two parts to explain whether or not the limit of s, exists. If the limit exists, find the limit.

(5) Consider the sequence defined by S1 = 1 Sn+1 = (sn +2) for n > 1 (a) Prove by induction 0 Sn <1 for all n E N (b) Prove the sequence is monotone. (c) Use the previous two parts to explain whether or not the limit of s, exists. If the limit exists, find the limit.

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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(5) Consider the sequence defined by -( + 2) for n21 S1 = 1 Sn+1 = (Sn 4 (a) Prove by induction for all n E N (b) Prove the sequence is monotone. (c) Use the previous two parts to explain whether or not the limit of s, exists. If the limit exists, find the limit.
Transcribed Image Text:(5) Consider the sequence defined by -( + 2) for n21 S1 = 1 Sn+1 = (Sn 4 (a) Prove by induction for all n E N (b) Prove the sequence is monotone. (c) Use the previous two parts to explain whether or not the limit of s, exists. If the limit exists, find the limit.
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