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Currently Playing: 5 ways to derive the general term of Fibonacci sequence

Matrix multiplication video: https://youtu.be/q1WRozg574k Previous video using generating function: https://youtu.be/Hl61mJxILA4 What if you are told to find the 100th Fibonacci number? Do you start from the first two terms? Wouldn't it be better if you know the general term of Fibonacci sequence, and just plug in n = 100 to obtain the answer? There are 4 different derivations presented in the video, and see which one is your favorite. I have also rated these methods in terms of satisfaction, and of course, I provided some reasons for the rating, but all these ratings are definitely just my opinions, and you have every right to disagree with me, and maybe tell me why in the comments! These methods include (1) just directly checking by induction, (2) characteristic equation for recurrence relations (i.e. combining geometric sequences as called in the video), (3) playing with the golden ratio phi, (4) matrix multiplication (shown in a separate video as linked above), and (5) generating function. All these are valid proofs, but they differ in the level of satisfaction! Mathematics is not just about whether something is right or wrong; it can also be about discovering a better, more satisfying proof. Sources: https://artofproblemsolving.com/wiki/index.php/Binet%27s_Formula (Penultimate derivation) https://www.quora.com/How-do-I-derive-Binets-Formula (First derivation) http://www.austinmohr.com/15spring4980/main.pdf (Ultimate derivation) Useful links: http://discrete.openmathbooks.org/dmoi2/section-27.html (More about generating functions) 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 #fibonacci #generalterm #binetformula #generatingfunction #goldenratio Video Chapters: 00:00 Intro 00:59 Checking by induction 02:12 Combining geometric sequences 04:17 From the golden ratio 05:47 Matrix multiplication 05:58 Generating function 09:29 Google form 10:06 Endcard stuff