Fibonacci's Explicit Equation: Binet's Formula

A natural derivation of the Binet's Formula, the explicit equation for the Fibonacci Sequence.

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[yashpatil]

I don't understand why this amazing video isn't getting popular..

[aliciazhi]

thank you for explaining this so intuitively! i like how this video shows why you try certain things / how problems are approached in math, it feels like being engaged with and not talked down at

[madhukiranattivilli]

This is the only youtube video or google article I could find where the binot's formula was PERFECTLY explained. Every article on the net (including wiki) just says "closed form expression" and doesn't explain. Thanks to this guy, who spoke about the 2 conditions :

(1) f(n+1) = a x f(n)
(this is assumed from f(n+1) = f(n) + f(n-1), and so f(n+1) > f(n), and assuming "a" as the factor separating the 2 fibonaccis)

(2) f(n) = g(n) + h(n)
(not really an assumption, but a deduction)

(3) f(1) = f(2) = 1 in fibonacci series.
This is slightly modified here to have f(0)=1 while dealing with (1) above, and f(0)=0 while dealing with (2) above.

Thanks very much!!!

[harshr]

This is great work.
I enjoyed and understood like its not a math...a story.
Great intuitive way to teach.
Keep going

[blueowl]

THIS IS SO SO HELPFUL THANK YOU SM FOR POSTING THIS YOU’RE AMAZING :)))

[aryadebchatterjee]

Great video dude, I think this is one of the very few videos that go at length making the binet-formula so natural

[phantom]

There are some videos explaining this on yt, but this one is the best.

[michellepark]

You are my role model. Your videos are very educational! Please post 😀

[oshinsamuel]

This account is legitimately going to get me through school

[branialtocci]

It's really an awesome way to evaluate this explicit formula. Well done

[RicardoDirani]

This made me understand the Binet formula. Thanks!

[mingyili]

Well explained video for interesting and complicated math problem. Please create more!

[madnorbi]

a(n) = 8*a(n-1)+9*a(n-2)
8*a(n-1) because: prepend one digit to the previous, any of the ten possible digits, except zero and the previous digit
9*a(n-2) because: prepend two digits to the previous, any of the ten possible digits except zero, followed by a zero
a(1) = 4 because we have four primes as the last digit (2, 3, 5, 7)
a(2) = 32 because a(2)=8*a(1)

[holyshit]

If we have given recurrence relation a_{n}=a_{n-1}+a_{n-2} but with different initial conditions we can express this sequence
it terms of the sequence F_{n}=F_{n-1}+F_{n-2}, F_{0}=0, F_{1}=1

[madhukiranattivilli]

About the problem at the end...

how is it :
a(n) = 8*a(n-1) + 9*a(n-2) ???

I got it as :
a(n) = 2^(3n - 1)

a1 = 4
a2 = 2^5 = 32
a3 = 2^8 = 256
a4 = 2^11 = 2048

how is it 2^(3n - 1) ???
for 1 digit: 2 3 5 7 are the possibilibies

for 2 digit numbers : ab
b is 2 or 3 5 7
ab is [^2]2 | [^3]3 | [^5]5 | [^7]7
8 possibilities in each set
so total of 8*4 = 32

for 3 digit numbers
abc
c is 2 or 3 or 5 or 7
for c=2
abc = [^b][^2]2 = #8 * #8 * 1 = 64
for 4 possibilities of c: 64*4 = 2^6 * 2^2 = 2^8 = 256

PLEASE COMMENT -- either the video provider or friends here

[etrenomics]

Issotjustme. Barry ktipke. A character on the television sitcom the big bang theory?

[auragula]

dude wtf? fibonacci starts with 0. 0, 1, 1, 2, 3, 5, ... etc

[sainadh]

The point is how do you guess the right functional form. The video is not helpful !!