Re: [math-fun] Binet's formula

Binet’s formula for the Fibonacci numbers follows fairly easily from the assumption that F_n=x^n, but I didn’t quite follow how/why one would make that guess.

Taking first differences gives the same sequence back. Differences are like derivatives. The function where taking the derivative with respect to n gives the same thing back is e^n. So look for something that's exponential in n. -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com