Is little phi (phi) being equal to the negative reciprocal of big phi (PHI) the reason that you put c1(PHI + phi) instead of c1(PHI - phi)? When you expand the former, you get c1PHI + c1phi, which is a different equation.
피보나치 수열(Fibonacci Sequence)의 일반항을 초간단 쉽고 빠르게 구하며 f(m+n-1) = f(m-1)f(n-1) + f(m)f(n). 그 외 피보나치 수열의 관련 공식들도 유도합니다. th-cam.com/video/656P79nawsA/w-d-xo.html
Find other Fibonacci and the Golden Ratio videos in my playlist th-cam.com/play/PLkZjai-2JcxleC9l3RjEG9yyV3XU9WLOc.html
good explanation, but you look like the villain in a james bond movie
Here we go craigfay.com/wp-content/uploads/2018/08/Blofeld-1-e1534175757812.jpg
at 5:20, how did you combine two solutions to create a general solution? can you please explain that or point to some resources which explain that?
It is called the Principle of Superposition. You can prove that the sum of two solutions is also a solution.
@@ProfJeffreyChasnov careful! this only works with linear functions
@@derda3209 That is correct!
Is little phi (phi) being equal to the negative reciprocal of big phi (PHI) the reason that you put c1(PHI + phi) instead of c1(PHI - phi)? When you expand the former, you get c1PHI + c1phi, which is a different equation.
phi=1/Phi = Phi-1. Both numbers are defined to be positive, with Phi = (sqrt(5)+1)/2 and phi=(sqrt(5)-1)/2.
teach so well that easy to understand. thx.
how do you know that it is the appropriate guess even before solving it !!
It is a well-known guess for linear difference equations. There is something similar for linear differential equations.
How du you get C2=-C1
no wonders teaching is free, cause it has no price!
Interesting, and there is a whole more . . . Maths Montage, Fibonacci.
Wonderful , Sir
😩 you lost me at Try Xn = ƛ^n
I thought I could handle this. I'm so illiterate in Math
appreciable & thanks..
피보나치 수열(Fibonacci Sequence)의 일반항을 초간단 쉽고 빠르게 구하며
f(m+n-1) = f(m-1)f(n-1) + f(m)f(n).
그 외 피보나치 수열의 관련 공식들도 유도합니다.
th-cam.com/video/656P79nawsA/w-d-xo.html
Lesson 5
Ok