The sequence {an} is defined by a1 = : 2, and An + An An+1 = for n > 1. Assuming that {an} converges, find its limit. lim an n00

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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The sequence {an} is defined by a1 =
= 2, and
17
1
an +
2
an+1
an
for n > 1. Assuming that {an} converges, find its limit.
lim an
Hint: Let a =
lim an. Then, since an+1=
2 (an + 2/an), we have
a = } (a + 2/a). Now solve for a.
Transcribed Image Text:The sequence {an} is defined by a1 = = 2, and 17 1 an + 2 an+1 an for n > 1. Assuming that {an} converges, find its limit. lim an Hint: Let a = lim an. Then, since an+1= 2 (an + 2/an), we have a = } (a + 2/a). Now solve for a.
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