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
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