What do Fibonacci numbers have to do with combinatorics?
Part II: • STAIRS reveal the relationship betwee...
Note: You ABSOLUTELY DON'T NEED TO HAVE KNOWN ANY COMBINATORICS because the combinatorics required in this video would be explained thoroughly.
Source of the beautiful thumbnail: https://www.videoblocks.com/video/win...
Usually we don't associate Fibonacci numbers with combinatorics (binomial coefficients), but here is a surprising relationship between the two, using the generating function of Fibonacci numbers.
Other useful links:
https://www.quora.com/How-would-you-s...
https://www.johndcook.com/blog/2018/0... (the comment is worth reading)
https://proofwiki.org/wiki/Fibonacci_... (A bit more rigorous proof of the relation shown, only if you are comfortable with all the binomial coefficients involved)
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#mathemaniac #math #combinatorics #fibonacci #generatingfunction #binomialcoefficients