partially summation

I want the delta_s[j]'s be summerized for every PART !
Can anyone help me ?

Code:

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define N 511

double funcwert(double a)
{
	return sqrt(1-a*a);
}
int main()
{	
	int i,k,j,PART;
	double delta_x, delta_y;
	double delta_s[N], sum=0.0;
	double p;
	FILE *f_ptr;
	f_ptr=fopen("/home/joerg/c_linint/src/dat.csv" , "w+");

	for(k=0 ; k<4 ; k++)
	{	PART=pow(2,k);
		
		 for(p=0.0, j=0; p<PART, j<PART; p++, j++) 
		
		{
			delta_x=(p+1)/PART - p/PART;
			delta_y=funcwert((p+1)/PART) - funcwert(p/PART);
			delta_s[j]=sqrt(delta_x*delta_x + delta_y*delta_y);
			
			
		}
	for (i=0;i<j;i++)
		{
			
			printf("%d	%d	%lf\n",PART, i, delta_s[i]);
			}
	
	for (i=0;i<j;i++) {
				sum=sum + delta_s[i];
					}
	printf("Summe=%lf\n",sum);	
	}
	
	//fprintf(f_ptr," ", );
	fclose(f_ptr);
  return 0;
}