Recent content by dyh

Thanks buddy! It is really helpful. I will try to get the specific form!

Hey guys, I would like to get some general form of recursive formula let f(s) = (a+bs)/(c+ds) given this I would like to get nth composite function of f i.e the general form of f^n(s)= fofofofofo...of(s) (nth composite) I can conjecture that the form of f^n(s) would be the same...

In my opinion, if I choose f(n)=f(n-1)=c for any non-negative integer n, then f(n+1) would be "c" too

oh.. I got some other general solution form f(n) = a+bn+n^2, a,b are constant But I still would like to know there would be more solutions or not. hehe

Thanks I know how to solve the general methods for solving recursions. But I think this is some special case of it because there is some contradiction in particular solution. I.e. when I put f(n)= c (constant) for non-negative integer n. then I can get c=(1/2)c+(1/2)c-1 so it looks like 0=-1...

Because if I differentiate A*(1+sqrt(5))^n with respect to n then I would get A*log(1+sqrt(5))*(1+sqrt(5))^n

f(n)=(1/2)f(n+1)+(1/2)f(n-1)-1 I got f(n)=n^2. I can not find anymore solution except this. I just wonder there are some more solutions about this problem or not. I think there are more, but I don't know how to get to them. I want to hear your opinion. Thanks

Homework Statement A>0, B can be any number Homework Equations To show that lim(n->∞) (1/n)log[A((1+sqrt(5))/2)^n +B((1-sqrt(5))/2)^n] = (1+sqrt(5))/2The Attempt at a Solution I used Lhopital's Rule to solve this and got log((1+sqrt(5))/2) So, I don't know what is wrong. If you guys...