From 43917e9750f7a57fc3d71e2f943a464af5f40ad7 Mon Sep 17 00:00:00 2001 From: fede Date: Thu, 19 Sep 2024 20:14:41 -0300 Subject: [PATCH] terminada entrega --- Discreta/entrega2.org | 20 +++++++++++++++----- Discreta/entrega2.pdf | Bin 0 -> 175766 bytes 2 files changed, 15 insertions(+), 5 deletions(-) create mode 100644 Discreta/entrega2.pdf diff --git a/Discreta/entrega2.org b/Discreta/entrega2.org index ab21f2f..61eddc3 100644 --- a/Discreta/entrega2.org +++ b/Discreta/entrega2.org @@ -2,8 +2,19 @@ #+author: Martin Luraschi, Luca Troiano, Roy Herrera, Federico Polidoro #+options: num:nil toc:nil * 1. - Dar los primeros cinco términos de una sucesión que verifique la relación derecurrencia a_n = n a_{n-1}. +- a_1 = 1 +- a_2 = 2 * a_1 = 2 * 1 = 2 +- a_3 = 3 * a_2 = 3 * 2 = 6 +- a_4 = 4 * a_3 = 4 * 6 = 24 +- a_5 = 5 * a_4 = 5 * 24 = 120 * 2. - Dar los primeros seis términos de una sucesión de términos positivos que verifique la relación de recurrencia a_n = a_{n-1} / a_{n-2}. + - a_1 = 1 + - a_2 = 2 + - a_3 = a_2 / a_1 = 2 / 1 = 2 + - a_4 = a_3 / a_2 = 2 / 2 = 2 + - a_5 = a_4 / a_3 = 1 / 2 = 1/2 + - a_6 = a_5 / a_4 = (1/2) / 1 = (1/2) * 3. - Dar los primeros cinco términos de una sucesión que verifique la relación de recurrencia a_n = a_{n-1} + n^2. 1. a^1 = a^{1-1} + 1^2 = 1 + 1 = 2 @@ -105,11 +116,10 @@ Se considerará que a^0 = 1, debido a que, como no hay mas metros que avanzar, l 6. a^6 = a^(6-1) + a^(6-2) = 8 + 5 = 13 -* 24 - Resolver las siguientes relaciones de recurrencias no homogéneas -- a. a_n - 3a_{n-1} = 5 7^n; a_0 = 2. -- b. a_{n+1} = a_n + 2^n; a_0 = 0. -- c. a_n = a_{n-1} + 3; a_0 = 1. -- d. a_{n+1} + 2a_n + a_{n-1} = n; a_0 = 1, a_1 = -1. * 25 - Un préstamo de $2500 se debe pagar en cuotas fijas mensuales de $300, con un interés mensual de 8%. Si an es el dinero adeudado en el mes n, plantear una relación de recurrencia para an. ¿En cuántos meses se saldará la deuda? +\begin{center} +a(n) = a(n-1) * 1,08 - 300 +\end{center} +En el mes 15 la deuda queda saldada diff --git a/Discreta/entrega2.pdf b/Discreta/entrega2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..aa59d32127f4a181879ebe8faf6967c71fa1c578 GIT binary patch literal 175766 zcma%?Q;;Z1m!-?L>y+!1ZQHhO+qP}nwr$(CZDVf7OwY^xBf9e`Gx9ap%C+~GNh~KM zLQPM@3`IP*G`t4Ij8BJeYhVGz#RWwxWo%>WWQNbi%7*`c2NbP{xs{W#13s;YmA;d) zkg=hykuekx50s;mgR#Cfl-tI%sX{fS>L4auFPtZNhp>DTU;U-#c3_2> zJT($!@ioxrtt-()c`{kd@rW5M8arbK>!aBHd@UM!s;!vu9#KHP)x9j3i1<*P`f(9) zCUs4NtU){{t-*Wo6m;OhE(!w;wC3g1PM%Pw)MFSQ)%}imKwPMXi z|Eua|@K5TN?Ip%#S|FJ&$zUc;Pfvv*MK(2_<5NMmP0hxd%dx#Vnev^wKan$r*js1M zaZbmS?n8htyLl{_zE~6#W{5&y3f58TcnKIFaI2U)zluds5~7h#T;NbTV(nxa*y=S0 ztc{_g;^=mj0S6yZPxKm9v%lM7mCH>f2X|{_3>a~x<#d`w`#1}= z^h)?`JJ?N$I)$|B$R$m9GvUgrF*DIQj+Bsc_Jcf_1Q=?bE?#tw>Ys&(Oq6yZ zIdZknZ#`U()ASi0i?Z3usCMUySh@taXy`Z<_)PE;BzmIyeNm;=_7Uy7Zlv~x8!Y}L zu$)GL)Pg&^U>ha<*ZRj2_jnUUfDJLjD+oXtQ9q{6N9lV*?!OCsao#_~OO7dWvxH-~ z%^;x&c0zIA#31uo59cTWPv;OWU4dujAv1PRY3$FLiWmiph;bq)fED7zk3_(rJoM`( z-*xutV^OjKXkYk7{jdTff!qX!za2JUpK3#E%aItI31Rnp^oWa)?Xjy)wDBtkEsK2f zHJQ?jmzoWWc^+JDWgb>n%CWn+mAITPZ1prH6Bv*MnM+hFgL+T0XZuAH54ga-Q3!;z zz0IHIwD3is`a4z8T$_q1+#XQ^``h6S^j1jf=>#V!$A**xeuM7X<-*NpgF=hzdUF$M1R&e zt7(3;w7%dg#?HNDxcBeHMRSwFwgO!AJQ*&mq;RIu}Hdc4>d!?{6kqficbe zH_EQ=XJJqvFSSh|f(TQ&ZyI+UP%;HH$0DWu`QB+aNm$@USy*&3F50a=bUQ0{_Ypg0snbd53e7~3z)d5x9hSa`4!|~=8j(Azf9vjMY zh%Q=Z23d46AL_QV6P<8A8+z+GnWfclD;$qlP~IP=4NihtCxXl=MFlidQ6&J%)mmfh zQ@w)hX|RI0y%LgxT$4zs^{A>91n#}S{a_cF z=pm5lVYI;%+|CJtQ1M{^;JLWY4e{?t@X0^JInwXLs;&nn>$PsAmbql;+ddUtmJ9Zh3FmNNNyjIdj z=4klmWJt@jhoFo*Xiit=FCR}7+3+kdD#P=-a4S0fC1hznupL<9C z%%TONbE?6JQHh+vpaD+@4@0naFq{k+1YsSb2|}8iCkz9CqNDvavNmY0KQaq;q8m2% z+mAK~Ss%p#c(~A8lZWQ=%RB+pYADTk%`5WV+PU6Gh8kttu2vnYXeiUt9htDYqC=_6${KuJpzq$Om(HY#Qw& zYMl)~QLBE$aSR_V^Ui#!t@I-e_#RKXJkn_e5bzOdQtM1FQ z&|wB7a2N;)k=+jxWN82-Fxqov3nRsMhOul8;AR5h zfu42uGO#QuHfN-?)-F+2Bgo{QzO~D27M#TLg^rfGPq6WBPKwI}GRN{q9?H1xGbdjs zskfz;DjkZLGRvWR;JT&0R*|FF>u1%a(CSC_>Y9n^No1RIrJgfPrwwf0kjAzH{X^&N z;KA^bdy9S4Iar;t)%weuP4XSTr}~F2$r^<{g&`%?U_W8a6jH;`DqX%158`)+{ z)cYpI3gxd)^@N9SRQK^d2f%GGfMcPxdj5$dWUQ!y0A41gsWP3RxSZ|F+->0;hnTgC8{)pcfbtt* za5#}WFGdjo_g@fROR?~*uDRq)dCE(O8KJybe3f1>(T#a?At(Fg@73E?KE7|qH;wrt zm1ocRX36}EPI=hxM8=6IyfaVk$2csE<#;MMA9FR$%PFa0*VZ3^I{`%lo9$4BC=KS{ z@w7Yb3A7|LMQX6=;?o+I+H*%qus#X>8Gc)59g_{1sKf2j6rg9ycl9(p9H)Q0D=kYY zOl#5;aN{9<#e;Yv5q?^abdmM73P`d5Oye^^!z1tn^dS>cNgDSM{TlR0gYLli4%M%G*^XA*3EH?S8BUcICud*L=|zx6#hUN-HY8v2dAfbKZAW^$cwVyEhJKv;`jLqjN3S!muZ1a^e0yKa?`I?OuHiSE zNgkaYTg7`reOleKey_`Ob+~$P;l6+DIVED8@0Wy7aX7{S5X%%X`aNhqj&)3L7WjL_O=V6xKpCQVu|#@>@~9cnOAfs5C- z+d;Kqpp*1v8|uKW%S5h>4NHKd1e0(gV%P?f01caSupvD{OxdU7S|PL-u+_BL%n^mS zbdJC`ZWk2Cfz(6nd|FDha;C)OuEsr))1c1T3DJ)7M@UDbarE_#Xn1Q)2_4hb`yuc! z#`F@@=~Vce+JhPM@6}e7=mI7eQbXta(>D^K#vm62TP1<3Yo62;Kj`_}sQ43uBOxcE z-W!^PnshF~r2w$BEmY zcd_U}keo+B0a(SGbRHB9B|x2NHz^|F6>5{l!Qo+|+~Tm*X^g{-)&Z#;pH_>5Q=x$t z6h8`bd=$ZJE2)&K*vM5HNje@L9NF(}6eO631^^^(!BG0|`$;x!{T zcK(>Z*)gXreRh*Er)_-Jju`HY%NcMuQZO61v+TdK>bIi{?4b+!u{DNrdqMc2WA>I-VL5JRY#W zSto~ZerAZX0x?X9clJJ-8trB>(GF5m6BUjr^ge(X1 zf8Yf!PhhlLdffB$946-e`SJ`A`3>r3(jdAhnk#$CKMXT6MwP=}kcy}I=FvE5Ino7? 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