fibonacci series for all the number using string

The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it. Similarly, the 3 is found by adding the two numbers before it (1+2).
                     By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.
In mathematical terms, the sequence F_n of Fibonacci numbers is defined by the recurrence relation

with seed values

or

Solution-

public int get FibonacciSeq(int n)

{

      if(n<-1) return -1;

      if(n==0) return 0;

      if(n==1|| n==2) return 1;

      int f0 = 0, f1 = 1;

      int result = 0;

      for (int k = 3; k <= n; k++) {

              result = f0 + f1;

              f0 = f1;

              f1 = result;

       }

       return result;

}

But the problem with above approach is there is range of n. Hence the number and the result should be in Integer range otherwise it will return -ive value. To solve this problem we can use below approach which takes input as integer and return String as a result.

public static String FibonacciSeq(int n) {

    if (n < 0)

         return "Not a valid Input";

    if (n == 0)

         return "0";

   if (n == 1 || n == 2)

         return "1";

    String f0 = "0";

    String f1 = "1";

    int k = 3;

    String out = "";

   while (k <= n) {

             out = "";

             int carry = 0;

             int c = 0;

             int i = f0.length() - 1, j = f1.length() - 1;

             for (; i >= 0 || j >= 0; i--, j--) {

                   if (i >= 0 && j >= 0) {

                         c = f0.charAt(i) - '0' + f1.charAt(j) - '0' + carry;

                   } else if (i >= 0) {

                         c = f0.charAt(i) - '0' + carry;

                   } else if (j >= 0) {

                         c = f1.charAt(j) - '0' + carry;

                    }

            out = (Integer.toString(c % 10)) + out;

            carry = c / 10;

       }

      if (carry != 0) {

          out = Integer.toString(carry) + out;

       }

      f0 = f1;

      f1 = out;

      k++;

 }

return out;

}