Fibonacci / Binomial coefficient identity

Here's an identity relating Fibonacci numbers and binomial coefficients.

You can think of it as a finite sum or an infinite sum: binomial coefficients are zero when the numerator is an integer and the denominator is a larger integer. See the general definition of binomial coefficients.

Source: Sam E. Ganis. Notes on the Fibonacci Sequence. The American Mathematical Monthly, Vol. 66, No. 2 (Feb., 1959), pp. 129-130

More Fibonacci number posts:

• Distribution of Fibonacci numbers mod m
• Inverse Fibonacci numbers
• Last digits of Fibonacci numbers
• Fibonacci numbers and orthogonal polynomials
• Honeybee genealogy