Mathc initiation/a505

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(" Ratio Test for Absolute Convergence.             \n\n");
 printf(" Let S.a_n be with non zero-term series.          \n\n");
 printf(" lim n->oo |a_n+1|/|a_n| < 1      The series converges absolutely\n"
        "                                      and therefore converges.\n");
 printf(" lim n->oo |a_n+1|/|a_n| > 1, +oo The series diverge \n");
 printf(" lim n->oo |a_n+1|/|a_n| = 1      Use another test \n\n");
 stop();

 clrscrn();
 printf(" |a_n|   : n-> |%s|           \n",     a_neq);
 printf(" |a_n+1| : n-> |%s|         \n\n", a_npls1eq);
 printf(" c_n     : n-> |a_n+1|/|a_n|\n\n");

 for(i=1; i<10; i++)
     printf(" c_%.0f = %5.3f || \n", i, fabs(a_npls1(i))/fabs(a_n(i)));
 
  printf(" \n\n\n"   
        " lim n->oo |a_n+1|/|a_n| = c < 1\n\n"      
        " the serie |a_n| absolutely converge"
        " and therefore a_n converges.\n\n");
 stop();

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

Exemple de sortie écran :

 Ratio Test for Absolute Convergence.                                       

 Let S.a_n be with non zero-term series.               

 lim n->oo |a_n+1|/|a_n| < 1      The series converges absolutely
                                      and therefore converges.
 lim n->oo |a_n+1|/|a_n| > 1, +oo The series diverge 
 lim n->oo |a_n+1|/|a_n| = 1      Use another test 

 Press return to continue.

Exemple de sortie écran :

 |a_n|   : n-> |(-1)**n *    3**n/    (2*n)!|           
 |a_n+1| : n-> |(-1)**n *   3**(n+1)/(2*(n+1))!|         

 c_n     : n-> |a_n+1|/|a_n|

 c_1 = 0.250 || 
 c_2 = 0.100 || 
 c_3 = 0.054 || 
 c_4 = 0.033 || 
 c_5 = 0.023 || 
 c_6 = 0.016 || 
 c_7 = 0.013 || 
 c_8 = 0.010 || 
 c_9 = 0.008 || 
 


 lim n->oo |a_n+1|/|a_n| = c < 1

 the serie |a_n| absolutely converge and therefore a_n converges.

 Press return to continue.