Fibonacci and Lucas Numbers with Applications, Volume 1, 2nd Edition

SOLUTIONS TO ODD-NUMBERED EXERCISES

EXERCISES 2

1. 1

   2.

2. 3

   .

3. 5

   .

4. 7

   .

5. 9

   We claim that , where . Since and , by PMI, the formula is true for .

6. 11

   .

7. 13

   .

8. 15

   .

9. 17

   The proof follows by PMI.

10. 19

    We have , where . Letting , , where . So , where .

11. 21

    (Brown) Suppose are in AP, so (say). ...