A sequence {an} is given by the recurrence relation (Show your work) a1 = V2. By mathematical induction, show that {a„} is nondecreasing and bounded An+1 /2 + an, Vn E N. above by 2. Deduce that {an} is a convergent sequence. B) Calculate lim an.
A sequence {an} is given by the recurrence relation (Show your work) a1 = V2. By mathematical induction, show that {a„} is nondecreasing and bounded An+1 /2 + an, Vn E N. above by 2. Deduce that {an} is a convergent sequence. B) Calculate lim an.
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:A sequence {an} is given by the recurrence relation (Show your work)
= v2,
,
V2 + аm, Hn EN.
аn+1
A)
By mathematical induction, show that {a,} is nondecreasing and bounded
above by 2. Deduce that {a„} is a convergent sequence.
B)
Calculate lim an.
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