Exercise 3. For a and b in R defined for 15, 2 by s we consider the Sequence Un = a + b Un-1 with Us za a) Show that S(Unti-un) (Un-Un-1) 20 [Tun+₁ = un] .

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Chapter2: Second-order Linear Odes
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Exercise 3.
For a and b in R", we consider the sequence
defined for 77,2 by:
Un = a t
b
Un-1
with U₁ za
a) Show that S(Unti-un) (Un-Un-1) 20
[Tunti-un| < |un-un-el
Cluaz
b7 show that the sequence (URn) is decreasing
and that the sequence (Vanti) is increasing.
Deduce that the sequence (Un) Converges.
Transcribed Image Text:Exercise 3. For a and b in R", we consider the sequence defined for 77,2 by: Un = a t b Un-1 with U₁ za a) Show that S(Unti-un) (Un-Un-1) 20 [Tunti-un| < |un-un-el Cluaz b7 show that the sequence (URn) is decreasing and that the sequence (Vanti) is increasing. Deduce that the sequence (Un) Converges.
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