Java - 278

import java.math.*;void m(String a){BigInteger i=null;BigInteger n=i.ONE;BigInteger d=n.add(n);BigInteger e=n;for(i=e;i.compareTo(i.valueOf(Integer.parseInt(a[0])))<0;i=i.add(e))do if((n=n.add(e)).compareTo(d)>=0)d=d.add(n=e);while(!n.gcd(d).equals(e));System.out.print(n+"/"+d);}}

Ungolfed:

import java.math.*;
void m(String args[]){
        BigInteger i=null;
        BigInteger n=i.ONE;
        BigInteger d=n.add(n);
        BigInteger e=n;
        for(i=e; i.compareTo(i.valueOf(Integer.parseInt(args[0])))<0; i=i.add(e))
            do
                if((n=n.add(e)).compareTo(d)>=0)
                    d=d.add(n=e);
            while(!n.gcd(d).equals(e));
        System.out.println(n +"/"+d);
    }
}

Original version

I have made no attempt to arbitrarily extend this solution. Not sure if that will gain me or lose me points. It is, however, a correct solution that will work for very large numbers.

public class Test {

    static class Fractions implements Iterator<String> {

        // Start at 1.
        BigInteger numerator = BigInteger.ONE;
        // Start at 2.
        BigInteger denominator = BigInteger.ONE.add(BigInteger.ONE);

        @Override
        public boolean hasNext() {
            // Never ending!
            return true;
        }

        @Override
        public String next() {
            String next = numerator + "/" + denominator;
            do {
                // Keep selecting the next one.
                step1();
                // Until they are relatively prime.
            } while (!numerator.gcd(denominator).equals(BigInteger.ONE));
            return next;
        }

        private void step1() {
            // Take a single step.
            numerator = numerator.add(BigInteger.ONE);

            if (numerator.compareTo(denominator) >= 0) {
                // num >= den - step denom up and num rewinds to 1.
                numerator = BigInteger.ONE;
                denominator = denominator.add(BigInteger.ONE);
            }
        }

    }

    // Returns the nth fraction.
    public String nthFraction(BigInteger n) {
        Iterator<String> f = new Fractions();
        for (BigInteger i = BigInteger.ONE; i.compareTo(n) < 0; i = i.add(BigInteger.ONE)) {
            f.next();
        }
        return f.next();
    }

    // Returns the nth fraction.
    public String nthFraction(long n) {
        return nthFraction(BigInteger.valueOf(n));
    }

    public void test() {
        Iterator<String> f = new Fractions();
        for (int i = 1; i < 100; i++) {
            System.out.println(i + "=" + f.next());
        }
    }

    public static void main(String args[]) {
        try {
            //new Test().test();
            if (args.length >= 1) {
                System.out.println(new Test().nthFraction(Integer.parseInt(args[0])));
            } else {
                System.out.println(new Test().nthFraction(5));
            }
        } catch (Throwable t) {
            t.printStackTrace(System.err);
        }
    }
}