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Binet's Formula

A special case of the $U_n$ Binet Form with $m=1$, corresponding to the $n$th Fibonacci Number,

F_n = {(1+\sqrt{5}\,)^n-(1-\sqrt{5}\,)^n\over 2^n\sqrt{5}}.

It was derived by Binet in 1843, although the result was known to Euler and to Daniel Bernoulli more than a century earlier.

See also Binet Forms, Fibonacci Number

© 1996-9 Eric W. Weisstein