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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
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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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 $\left(X_{n}\right)_{n \geqslant 1}$.

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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. -
Transcribed Image Text: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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