# include <stdio.h>
# include <math.h>
 
 
 
const int     i_Initial    = 1 ;
const int     i_Final      = 15 ;
 
double si_Formula( int i ){
    return (
    		88./60*pow(0.12,i) +
    		89./55*pow(0.11,i) +
    		90./50*pow(0.10,i) +
    		91./45*pow(0.09,i) +
    		92./40*pow(0.08,i)
		)/( 1-16e-17 ) ;
}
 
 
 
int main(){
    double Si_Infinite=0 , Sip1=0 , Si=Sip1-si_Formula(i_Initial-1) , Sim1=Si-si_Formula(i_Initial-2) ;
    for( int i=i_Final+999 ; i>=i_Initial ; i-- ) Si_Infinite+=si_Formula(i) ;
    for( int i=i_Initial-1 ;;){
        # define Abs(x)   ((x)<0?-(x):(x))
        # define Max(x,y) ((x)>(y)?(x):(y))
        double Sip1_Error = Abs(Sip1-Si_Infinite)/(Max(Sip1,Si_Infinite)+5e-324) ;
        double Expected_Si_Infinite = Sip1-( Sip1-Si )*( Sip1-Si )/( Sip1+Sim1-Si-Si  ) ;
        double Expected_Si_Infinite_Error = Abs(Expected_Si_Infinite-Si_Infinite)/(Max(Expected_Si_Infinite,Si_Infinite)+5e-324) ;
        printf( "S_%03i =%12.9lf (%.2e)  |  DeltaSquared S_%03i =%12.9lf (%.2e)"
                , i+1
                , Sip1
                , Sip1_Error
                , i+1
                , Expected_Si_Infinite
                , Expected_Si_Infinite_Error
            ) ;
        if( ++i > i_Final ){ printf("  S_Inf = %.16lf",Si_Infinite) ; return 0 ; }
        double si = si_Formula(i) ;
        Sim1=Si , Si=Sip1 , Sip1+=si ;
        printf( "  |-->  s%03i =%14.11lf\n" , i , si ) ;
    }
}

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