Mathc initiation/a504

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c00a.c

/* ---------------------------------- */
/* save as c00a.c                     */
/* ---------------------------------- */
#include "x_afile.h"
#include      "fa.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 *   (n**2   +4)/  2**n|           
 |a_n+1| : n-> |(-1)**n *  ((n+1)**2+4)/ 2**(n+1)|         

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

 c_1 = 0.800 || 
 c_2 = 0.812 || 
 c_3 = 0.769 || 
 c_4 = 0.725 || 
 c_5 = 0.690 || 
 c_6 = 0.662 || 
 c_7 = 0.642 || 
 c_8 = 0.625 || 
 c_9 = 0.612 || 
 


 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.