Add new file

recursive code

+#include <stdio.h>
+#include <math.h>
+#include <stdlib.h>
+
+#define MAX_LAYERS 15
+
+double calculateA(int L, double X);
+void calculateArrayRecursive(double X, double* A, double e, int L, int* numLayers);
+void getInput(double* X, double* e);
+void saveToFile(double* A, int numLayers);
+
+int main() {
+    double X, e, A[MAX_LAYERS];
+    int numLayers = 0;
+    
+    getInput(&X, &e);
+    calculateArrayRecursive(X, A, e, 1, &numLayers);  
+    saveToFile(A, numLayers);
+    
+    return 0;
+}
+
+void getInput(double* X, double* e) {
+    printf("Enter the value of X (|X| < 1): ");
+    scanf("%lf", X);
+    
+    printf("Enter the value of e (0 < e < 1): ");
+    scanf("%lf", e);
+    
+    if (fabs(*X) >= 1 || *e <= 0 || *e >= 1) {
+        printf("Invalid input! Ensure |X| < 1 and 0 < e < 1.\n");
+        exit(1);
+    }
+}
+
+double calculateA(int L, double X) {
+    double term = 1.0;
+    for (int i = 1; i < L; i++) {
+        term *= (2 * i - 1) / (double)(2 * i);
+    }
+    double A_L = pow(X, 2 * L - 1) * term / (2 * L - 1);
+    A_L *= pow(-1, L + 1);
+    return A_L;
+}
+
+void calculateArrayRecursive(double X, double* A, double e, int L, int* numLayers) {
+    if (L > MAX_LAYERS) return;  
+    A[L - 1] = calculateA(L, X);  
+    if (L > 1 && fabs(A[L - 1] - A[L - 2]) > e) { 
+        printf("Stopping at L = %d because |A_L - A_{L-1}| > e\n", L);
+        return;  
+    }
+
+    (*numLayers)++; 
+    calculateArrayRecursive(X, A, e, L + 1, numLayers); 
+}
+
+void saveToFile(double* A, int numLayers) {
+    FILE *f = fopen("F.txt", "w");
+    if (f == NULL) {
+        printf("Error opening file.\n");
+        exit(1);
+    }
+    
+    fprintf(f, "Number of elements: %d\n", numLayers);
+    for (int i = 0; i < numLayers; i++) {
+        fprintf(f, "A%d = %.10lf\n", i + 1, A[i]);
+    }
+    fclose(f);
+    printf("Results saved to F.txt\n");
+}