Consider the sequence recursively defined by the relation = 1/2 (a₁ + 12/12) an an an+1 = 00=-1 and assume that lim an exists. x→00 Find all fixed points of (an), and use a table or other reasoning to guess which fixed point is the limiting value for the given initial condition.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider the sequence recursively defined by the relation
1
an +
2
an+1 =
an
ao = -1
and assume that lim an exists. x→
Find all fixed points of (an), and use a table or other reasoning to guess which fixed point is the
limiting value for the given initial condition.
Transcribed Image Text:Consider the sequence recursively defined by the relation 1 an + 2 an+1 = an ao = -1 and assume that lim an exists. x→ Find all fixed points of (an), and use a table or other reasoning to guess which fixed point is the limiting value for the given initial condition.
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