Consider the sequence x_0 = 4, x_n = sqrt{6 + x_n−1} for n ≥ 1. (Note that the definition of the general term is the same as in the previous exercise, however the initial value is different). P-7.1 Show that the

Consider the sequence , for n ≥ 1.

Resuelto Consider the sequence x_0 = 4, x_n = sqrt{6 + x_n−1}

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Pregunta: Consider the sequence x_0 = 4, x_n = sqrt{6 + x_n−1} for n ≥ 1. (Note that the definition of the general term is the same as in the previous exercise, however the initial value is different). P-7.1 Show that the

Consider the sequence x_0 = 4, x_n = sqrt{6 + x_n−1} for n ≥ 1. (Note that the definition of the general term is the same as in the previous exercise, however the initial value is different).

P-7.1 Show that the sequence is lower bounded by 3.

P-7.2 Study the monotonicity of the sequence and conclude on its convergence.

Muestra el texto de la transcripción de la imagen
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Solución
Paso 1
Consider the sequence
$\begin{aligned} x_{0} & = 4 \end{aligned}$
,
$\begin{aligned} x_{n} & = \sqrt{6 + x_{n - 1}} \end{aligned}$
for n ≥ 1.
Mira la respuesta completa
Paso 2
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Paso 3
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Respuesta
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Texto de la transcripción de la imagen:

Ejercicio 7. Considere la sucesión

x_{0} = 4, x_{n} = 6 + x_{n - 1}

para

n \geq 1

. (Nótese que la definición del término general es la misma que la del ejercicio anterior, sin embargo el valor inicial es distinto). P-7.1 Muestre que la sucesión es acotada inferiormente por 3 .

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Pregunta: Consider the sequence x_0 = 4, x_n = sqrt{6 + x_n−1} for n ≥ 1. (Note that the definition of the general term is the same as in the previous exercise, however the initial value is different). P-7.1 Show that the

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