Uploads from Mathemaniac

Currently Playing: What do Fibonacci numbers have to do with combinatorics?

Part II: https://youtu.be/_RHXmGWXUvw 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/winter-stargate-deep-space-fibonacci-spiral-infinite-zoom-scl2tvcpliylych5s 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-show-that-sum-limits_-k-1-infty-frac-F_-k-x-k-frac-x-x-2-x-1/answer/Trevor-Cheung https://www.johndcook.com/blog/2018/02/22/fibonacci-binomial-coefficient-identity/ (the comment is worth reading) https://proofwiki.org/wiki/Fibonacci_Number_as_Sum_of_Binomial_Coefficients#Proof (A bit more rigorous proof of the relation shown, only if you are comfortable with all the binomial coefficients involved) Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! #mathemaniac #math #combinatorics #fibonacci #generatingfunction #binomialcoefficients