From 1973750c5fb147f6b7e021a3601355834c836b0a Mon Sep 17 00:00:00 2001 From: fede Date: Thu, 19 Sep 2024 20:54:41 -0300 Subject: [PATCH] listo no pienso subir los 20 pngs de roy --- Discreta/entrega2.org | 78 ++++++++++++++++++++++++++++++++++++++++++ Discreta/entrega2.pdf | Bin 175766 -> 366936 bytes 2 files changed, 78 insertions(+) diff --git a/Discreta/entrega2.org b/Discreta/entrega2.org index 61eddc3..d313b54 100644 --- a/Discreta/entrega2.org +++ b/Discreta/entrega2.org @@ -64,28 +64,106 @@ a_5 = (5+1)a_{5-2} = 6 * a_{3} = 6 * 4 * a_{1} = 6 * 4 * 2 * a_{-1} = ... * 8. - Resolver las relaciones de recurrencia - a. a_n-2/3 a_{n-1} = 0, n \geq 1; a_0 = -1 + \begin{center} +a_{n} = \frac{2}{3} a_{n-1} + +a_{1} = -\frac{2}{3} + +a_{2} = \frac{2}{3} \left( -\frac{2}{3} \right) = -\frac{4}{9} + +a_{3} = -\frac{8}{27} + \end{center} + - b. 2 a_n+1-3 a_n = 0, n \geq 0; a_0 = 1 + \begin{center} +a_{n+1} = \frac{3}{2} a_{n} + +a_{n} = \frac{3}{2} a_{n-1} + +a_{n} = \left( \frac{3}{2} \right)^n a_{0} + +a_{n} = \left( \frac{3}{2} \right)^n + \end{center} + - c. 2 a_n+1-3 a_n = 0, n \geq 0; a_0 = -2 + \begin{center} +a_{n} = (-2) \left( \frac{3}{2} \right)^{n} + + \end{center} + - d. a_n+1 - 5a_n + 6a_{n-1} = 0 n \geq 1; a_0 = 0, a_1 = 2 + \begin{center} +r^2 - 5r + 6 = 0 + +(r - 2)(r - 3) = 0 + +a_n = A * 2^n + B * 3^n + +a_0 = A * (2)^0 + B * (3)^0 = A + B = 0 + +A = -B + +a_1 = A * (2)^1 + B * (3)^1 = A2 + B3 = 2 + +A2 + B3 = 2 + +(-B)2 + B3 = 2 + +B = 2 + +A = -B = -2 + +a_n = -2*2^n+2*3^n + \end{center} + - e. a_n+1 = 4a_n - 5a_{n-1}, n \geq 1; a_0 = -1, a_1 = 3 + \begin{center} +Uh... + \end{center} + - f. a_n = 4 a_{n-1} - 4a_{n-2}, n \geq 2; a_0 = 6, a_1 = 8 + \begin{center} +a_n = (6-2n) * 2^n + \end{center} + - g. a_n = 2a_{n-1} - a_{n-2}, n \geq 2; a_0 = 1, a_1 = 2 + \begin{center} +a_n = 1 + n + \end{center} + * 9. - Dada la relación de recurrencia 8 a_{n+2} + 4 a_{n+1} - 4 a_n = 0. n \leq 0; Indicar si las siguientes sucesiones pueden ser solución: - a. a_n = 3 (-1)^n +[[./formula que estaba en formato chinhenhonshin hecha por roy 1.png]] + - b. a_n = 3 (-1/2)^n +1 +[[./formula que estaba en formato chinhenhonshin hecha por roy 2.png]] + - c. a_n = 4 (-1)^n + (1/2)^n +[[./formula que estaba en formato chinhenhonshin hecha por roy 3.png]] + - d. a_n = -4 (1)^n + (1/2)^n +[[./formula que estaba en formato chinhenhonshin hecha por roy 4.png]] + En caso afirmativo, justificar e indicar cuáles serían las condiciones iniciales que hay que imponer para obtener dicha solución. En caso negativo, justificar. * 10 - Dada la relación de recurrencia a_{n+2} − a_n = 0, indicar si las siguientes sucesiones pueden ser solución: - a. a_n = 3(−1)^n +[[./formula que estaba en formato chinhenhonshin hecha por roy 5.png]] + - b. a_n = 3(−1/2)^n + 1 +[[./formula que estaba en formato chinhenhonshin hecha por roy 6.png]] + - c. a_n = 7 + 2(−1)^n +[[./formula que estaba en formato chinhenhonshin hecha por roy 7.png]] + - d. a_n = 1/3 2^n +[[./formula que estaba en formato chinhenhonshin hecha por roy 8.png]] + - e. a_n = −8 +[[./formula que estaba en formato chinhenhonshin hecha por roy 9.png]] En caso afirmativo, justificar e indicar cuáles serían las condiciones iniciales que hay que imponer para obtener dicha solución. 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