Let a E R and the sequence: Ja ;n = 1 x-1+6x-1+ 12xn-1 + 6; n > 2 Xn a)Show that for every n E N; n > 1,this equality take place, Xn b) Calculate the limit af the sequence (Xn)n>1• (а + 2)3" — 2. -

Let a E R and the sequence: Ja ;n = 1 x-1+6x-1+ 12xn-1 + 6; n > 2 Xn a)Show that for every n E N; n > 1,this equality take place, Xn b) Calculate the limit af the sequence (Xn)n>1• (а + 2)3" — 2. -

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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Question

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Let $\alpha \in \mathbb{R}$ and the sequence:
$$
X_{n}=\left\{\begin{array}{l}
\alpha \quad ; n=1 \\
x_{n-1}^{3}+6 x_{n-1}^{2}+12 x_{n-1}+6 ; n \geqslant 2
\end{array}\right.
$$
a)Show that for every $n \in \mathbb{N} ; n \geqslant 1$,this equality take place, $X_{n}=(a+2)^{{3}^{{n-1}}}-2$.
b) Calculate the limit af the sequence $\left(X_{n}\right)_{n \geqslant 1}$.

Please check the attached picture for details.

I need complete solution with explanation, thanks in advance.

Let a E R and the sequence:
Ja ;n = 1
Xn
x-1+6x-1+ 12xn-1 + 6; n > 2
p3
п-1
a)Show that for every n E N; n > 1,this equality
take place, Xn
b) Calculate the limit af the sequence (Xn)n>1•
(а + 2)3" — 2.
-

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