(C programming) Writing the Leibniz method using a WHILE loop - c

Question

The purpose of my assignment is to create a FOR loop that performs the circle method of getting pi and a WHILE loop that performs the Leibniz method for approximating Pi. I have no idea where to start for the Leibniz method because I don't understand what expression to put in the while loop to make it work. Please help me.
This method approximates pi by using a formula derived by Gottfried
Leibniz, also known as "the father of calculus." This method uses an
infinite series of additions and subtractions to approximate pi:
π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + . . .
Notice that this approximates pi / 4. After the summation of the
terms, you need to multiply the value by 4 to arrive at the final
approximation. Analogous to the circle method, the more terms in the
series, the closer the approximation of pi: (Example)
Iterations Leibniz Method
1 4.000000000000
10 3.041839618929
100 3.131592903559
1000 3.140592653840
10000 3.141492653590
100000 3.141582653590
I have already completed the circle method for loop, and it works on its own. It's the while loop that the focus should be on.
double circle_pi(int rectangles)
{
double radius = 2.0;
long i;
long double width = radius / (long double)rectangles;
long double rect_area = 0.0;
long double midpoint, height;
midpoint = width / 2.0;
for(i = 1; i <= rectangles; i++)
{
height = sqrt((radius * radius) - (midpoint * midpoint));
midpoint = midpoint + width;
rect_area = rect_area + width * height;
}
return rect_area;
}
double leibniz_pi(int iterations)
{
while()
{
/* code */
}
return
}
This is my driver.c code to go with it. I cannot make changes to it.
double circle_pi(int rectangles); /* Calculates PI using a quarter circle */
double leibniz_pi(int iterations); /* Calculates PI using a series */
int main(void)
{
int i; /* loop counter */
/* Print out table header */
printf("Approximations for pi\n");
printf("Iterations Circle Method Leibniz Method\n");
printf("----------------------------------------------\n");
/* Print out values for each set of numbers */
for (i = 1; i <= 1000000; i *= 10)
{
/* Calculate PI with both methods */
double pi_circle = circle_pi(i);
double pi_leibniz = leibniz_pi(i);
/* Print the results of the calculations */
printf("%10i%20.12f%16.12f\n", i, pi_circle, pi_leibniz);
}
return 0; /* Return success to the OS */
}```

Answer 1

The Leibniz method subtracts and adds fractions with odd denominators alternately.
Thus, our code will look something like the following:
int count = 0;
int iters = 10000;
double pi_4 = 0;
while (count < iters) {
if (count % 2 == 0) {
// On "even" counts (where our fraction is 1/1, 1/5, 1/9..., add)
pi_4 += 1.0 / (1.0 + 2 * count);
else {
// On "odd" counts (where our fraction is 1/3, 1/7, 1/11..., subtract)
pi_4 -= 1.0 / (1.0 + 2 * count);
}
count++;
}
return 4 * pi_4;