5 + 8 = 13

Smokestack in Turku, Finland |

This problem was studied and solved by a famous mathematician,
Fibonacci. The numbers of rabbits form the **Fibonacci series**.
This series has important applications in several problems
that have nothing to do with rabbits.
Call the N'th number in the series `fib(N)`

:

Fibonacci Series | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

N | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

fib(N) | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 |

Here is the rule for filling the chart, rewritten for `fib(N)`

:

fib( N ) = fib( N-1 ) + fib( N-2 )

Look at the chart to verify that the rule works.