Click here to download contfrac.c.

/**********************************************
For integer a, we have the following continued
fraction:

a + 1/(a + 1/(a + 1/(a + ...

Of course this is an infinite continued fraction,
so we could also define f(a,n) to be the first n
terms, so that:
f(a,0) = a
f(a,1) = a + 1/a
f(a,2) = a + 1/(a + 1/a)
...
Implement f(a,n) recursively.
 **********************************************/
#include <stdio.h>

double f(int a, int n);

int main() {
  // Get integer n, n >= 0
  int n, a;
  printf("Enter non-negative integer: ");
  fflush(stdout);
  scanf(" %i", &n);
  printf("Enter value a: ");
  fflush(stdout);
  scanf(" %i", &a);

  printf("f(%i, %i) = %.20g\n", a, n, f(a,n));

  return 0;
}

double f(int a, int n) {
  if (n == 0) {
    return a;
  }
  else {
    return a + 1/f(a,n-1);
  }
}