Mathc initiation/a387

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00b.c

/* ---------------------------------- */
/* save as c00b.c                     */
/* ---------------------------------- */
#include "x_afile.h"
#include      "fb.h"
/* ---------------------------------- */
int main(void)
{
double i;

 clrscrn();
 printf(" Limit comparison test.                               \n\n\n");
 printf(" Let S.a_n and S.b_n be positive-term series.           \n\n");
 printf(" If there is a positive real number c such that       \n\n\n");
 printf("         lim n->oo (a_n/b_n) = c >0                     \n\n\n");
 printf(" The either both series converge or both series diverge.\n\n");
 stop();

 clrscrn();
 printf("# Copy and past this file into the screen of gnuplot\n\n"
        "  set zeroaxis lt 3 lw 1\n"
        "  set grid\n"
        "  plot [0.:20.] [-.01:0.1]\\\n"
        "  %s,\\\n"
        "  %s\n\n"
        "  reset\n\n",a_xeq, b_xeq);   
 stop();

 clrscrn();
 printf(" a_n : n-> %s\n\n", a_neq);
 printf(" b_n : n-> %s\n\n", b_neq);
 printf(" c_n : n-> a_n/b_n\n\n");

 for(i=1; i<10; i++)
     printf(" c_%.0f = %5.3f || c_%.0f = %5.6f || c_%.0f = %5.8f\n",
     i,        a_n(i)/b_n(i),
     i*10,  a_n(i*10)/b_n(i*10),
     i*100,a_n(i*100)/b_n(i*100) );
     
 printf("\n\n");
 stop();

 clrscrn();
 printf(" a_n : n-> %s  \n\n", a_neq);
 printf(" b_n : n-> %s\n\n\n", b_neq);
 printf(" Since S.b_n is a convergence geometric series (r=n<1).\n\n");
 printf(" It follows from the theorem that S.a_n is     \n\n");
 printf(" also converge.                              \n\n\n");

 stop();

 return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */

Exemple de sortie écran :

 Limit comparison test.                               


 Let S.a_n and S.b_n be positive-term series.           

 If there is a positive real number c such that       


         lim n->oo (a_n/b_n) = c >0                   


 The either both series converge or both series diverge.

 Press return to continue.

Exemple de sortie écran :

# Copy and past this file into the screen of gnuplot

  set zeroaxis lt 3 lw 1
  set grid
  plot [0.:20.] [-.01:0.1]\
  (3*x**2 + 5*x) / ((2**x)*x**2 + 2**x),\
  1/2**x

  reset 
 Press return to continue.

Exemple de sortie écran :

 a_n : n-> (3*n**2 + 5*n) / ((2**n)*n**2 + 2**n)

 b_n : n-> 1/2**n

 c_n : n-> a_n/b_n

 c_1 = 4.000 || c_10 = 3.465347 || c_100 = 3.04969503
 c_2 = 4.400 || c_20 = 3.241895 || c_200 = 3.02492438
 c_3 = 4.200 || c_30 = 3.163152 || c_300 = 3.01663315
 c_4 = 4.000 || c_40 = 3.123048 || c_400 = 3.01248117
 c_5 = 3.846 || c_50 = 3.098760 || c_500 = 3.00998796
 c_6 = 3.730 || c_60 = 3.082477 || c_600 = 3.00832498
 c_7 = 3.640 || c_70 = 3.070802 || c_700 = 3.00713672
 c_8 = 3.569 || c_80 = 3.062022 || c_800 = 3.00624530
 c_9 = 3.512 || c_90 = 3.055178 || c_900 = 3.00555184


 Press return to continue.

Exemple de sortie écran :

 a_n : n-> (3.*pow(n,2.)+5.*n) / (pow(2.,n)*pow(n,2.)+pow(2.,n))  

 b_n : n-> 1./pow(2.,n)


 Since S.b_n is a convergence geometric series (r=n<1).

 It follows from the theorem that S.a_n is     

 also converge.                              


 Press return to continue.