Binet's Formula: In Action

Suppose that we want to find out what the 50th Fibonacci number is without writing out the entire series. For this we would use Binet's Formula:

We would first plug 50 in for x in the formula:

This expression then reduces as follows:

Thus we see that the 50th Fibonacci number is 12586269025. If you feel like writing and adding for a while, you can check this by calculating all previous 49 Fibonacci numbers. Of course, the formula was created in the first place so you wouldn't have to do just that!