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c00c.c
/* ---------------------------------- */
/* save as c00c.c                     */
/* ---------------------------------- */
#include "x_afile.h"
#include      "fc.h"
/* ---------------------------------- */
int main(void)
{
double i;

 clrscrn();
 printf(" Alternating series \n\n"
        "  ----                          ----            \n"
        "  \\                             \\             \n"
        "  | (-1)**(n+1) * a_n           | (-1)**n * a_n \n"         
        "  /                             /               \n"        
        "  ----                          ----            \n\n\n\n");
       
 printf(" Alternating series test\n\n"
        " a) If a_n >= a_(n+1) > 0 for every n,\n\n"
        "            and\n\n" 
        " b) If lim n->oo a_n = 0\n\n"
        "      The series converge\n\n\n");
        
               
 stop(); 
 
 clrscrn();
 printf(" Alternating series test\n\n"
        " a) If a_n >= a_(n+1) > 0 for every n,\n\n"
        " Remark : \n\n"
        " if a_n = f(n), you can use f'(x) < 0 to verify a)\n\n"
        "            or\n\n" 
        " a_n - a_(n+1) >= 0\n\n"
        "            or\n\n"         
        " a_(n+1) / a_n =< 1\n\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 || c_%.0f = %+5.3f || c_%.0f = %+5.6f\n",
     i,      a_npls1(i)      /a_n(i),
     i*10,   a_npls1(i*10)   /a_n(i*10),
     i*10000,a_npls1(i*10000)/a_n(i*10000));
          
 printf(" \n\n\n"
        " c_n = a_(n+1)/a_n =< 1\n\n\n");
 stop();

 clrscrn(); 

 printf(" lim n->oo a_n = 0 \n\n");
         
 for(i=2; i<10; i++)
     printf(" a_%.0f = %+5.3f || a_%.0f = %+5.3f || a_%.0f = %+5.6f\n",
     i,      a_n(i),
     i*10,   a_n(i*10),
     i*10000,a_n(i*10000));
         
 printf(" \n\n\n"   
        " The series converge\n\n");
 stop();

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


Exemple de sortie écran :

 Alternating series 

  ----                          ----            
  \                             \             
  | (-1)**(n+1) * a_n           | (-1)**n * a_n 
  /                             /               
  ----                          ----            



 Alternating series test

 a) If a_n >= a_(n+1) > 0 for every n,

            and

 b) If lim n->oo a_n = 0

      The series converge


 Press return to continue.


Exemple de sortie écran :

 Alternating series test

 a) If a_n >= a_(n+1) > 0 for every n,

 Remark : 

 if a_n = f(n), you can use f'(x) < 0 to verify a)

            or

 a_n - a_(n+1) >= 0

            or

 a_(n+1) / a_n =< 1


 Press return to continue.


Exemple de sortie écran :

 a_n     : n-> ( n   +4) / ( n*   ( n   -1))         
 a_(n+1) : n-> ((n+1)+4) / ((n+1)*((n+1)-1))         

 c_n     : n-> a_(n+1)/a_n

 c_1 = +0.000 || c_10 = +0.877 || c_10000 = +0.999900
 c_2 = +0.389 || c_20 = +0.942 || c_20000 = +0.999950
 c_3 = +0.571 || c_30 = +0.963 || c_30000 = +0.999967
 c_4 = +0.675 || c_40 = +0.973 || c_40000 = +0.999975
 c_5 = +0.741 || c_50 = +0.979 || c_50000 = +0.999980
 c_6 = +0.786 || c_60 = +0.982 || c_60000 = +0.999983
 c_7 = +0.818 || c_70 = +0.985 || c_70000 = +0.999986
 c_8 = +0.843 || c_80 = +0.987 || c_80000 = +0.999987
 c_9 = +0.862 || c_90 = +0.988 || c_90000 = +0.999989
 


 c_n = a_(n+1)/a_n =< 1


 Press return to continue.


Exemple de sortie écran :

 lim n->oo a_n = 0 

 a_2 = +3.000 || a_20 = +0.063 || a_20000 = +0.000050
 a_3 = +1.167 || a_30 = +0.039 || a_30000 = +0.000033
 a_4 = +0.667 || a_40 = +0.028 || a_40000 = +0.000025
 a_5 = +0.450 || a_50 = +0.022 || a_50000 = +0.000020
 a_6 = +0.333 || a_60 = +0.018 || a_60000 = +0.000017
 a_7 = +0.262 || a_70 = +0.015 || a_70000 = +0.000014
 a_8 = +0.214 || a_80 = +0.013 || a_80000 = +0.000013
 a_9 = +0.181 || a_90 = +0.012 || a_90000 = +0.000011
 


 The series converge

 Press return to continue.