Вычисление суммы ряда с заданной погрешностью

...
double Eps;
cout<<"Input Eps:";
cin>>Eps;
double ArcTan=0, S=1; int n=0;
while(abs(S-S_pred)>Eps)
      {
      n++;
      S_pred=S;
      S=(-1^n)*(x^(2n+1)/(2n+1));
      ArcTan+=S
      }
...

...
double Eps;
cout<<"Input Eps:";
cin>>Eps;
double S=1; int n=0;
while(abs(atan(x)-S)>Eps)
      {
      n++;
      S+=pow(-1,n)*(pow(x,(2n+1))/(2n+1));
      }
...

double arctanx_(double x, double eps, int n, double f_prev, double chislit)
{
    double cur_item = chislit / (2*n + 1);
    double f = f_prev + cur_item;
 
    if(n > 0 && fabs(f - f_prev) < eps)
        return f;
 
    return arctanx_(x, eps, n + 1, f, chislit * (-1) * x * x);
}
 
double arctanx(double x, double eps)
{
    return arctanx_(x, eps, 0, 0, x);
}

#include<stdio.h>
#include<conio.h>
#include<math.h>
 
float ArcTang(float x1, int n1);
float ArcTangRek(float xn, int n1, int n2);
int GetN(float x1, float eps);
 
int main(void)
{
const int N = 100;
float x, y, eps;
int n, menu;
while (1)
{
clrscr();
puts("Choose the action: \n1. Input x and calculate y=arctg(x) on a recurrent parity\n (Iteratonal functon)\n2. Input x and calculate y=arctg(x) on a recurrent parity\n (Recurrent functon)\n3. Input x, e and find out, how many iterations are necessary to execute,\n that the parity was carried out: IY(n)-Y(n+1)I<e\n4. Exit programm");
scanf("%d",&menu);
switch (menu)
{
case 1:
{
puts("Enter x.");
scanf("%f", &x);
y = ArcTang(x, N);
printf("Result:\ny=%f", y);
getch();
break;
}
case 2:
{
puts("Enter x.");
scanf("%f %f", &x);
y = ArcTangRek(x, 0, N);
printf("Result:\ny=%f", y);
getch();
break;
}
case 3:
{
puts("Enter x, e through the gap.");
scanf("%f %f", &x, &eps);
n = GetN(x, eps);
printf("Result:\nn=%f", n);
getch();
break;
}
case 4:
{
puts("Thanks for using my programm!");
getch();
return 1;
}
default:
{
puts("Incorrect input!");
getch();
break;
}
}
}
}
 
float ArcTang(float x1, int n1)
{
int i = 0;
float s = 0, xn = x1;
while (i < n1)
{
s += xn;
xn *= xn*xn*(-1)/(2*i+3);
i++;
}
}
 
float ArcTangRek(float xn, int n1, int n2)
{
if (n1 == n2)
{
return xn;
}
else
{
return xn+ArcTangRek(xn, n1+1, n2);
xn *= xn*xn*(-1)/(2*n1+3);
}
}
 
 
int GetN(float x1, float eps1)
{
float y1, y2;
int n1 = 0;
y1 = ArcTang(x1, 0);
y2 = ArcTang(x1, 1);
while (fabs(y1-y2)>eps1)
{
y1 = y2;
n1++;
y2 = ArcTang(x1, n1+1);
}
return n1;
}