recursive formulas I'm studying linear algebra. I don't know how to deal with recursive formulas, for example


*

*fibonacci

*when you should find a big determinant of size $n$  (I think Vandermonde uses a recursive formula is found there, or is it induction?) 

*how do you go from a recursive formula to an explicit one?


Bad question, but I do need some guidance here. 

The Fibonacci function is as follows:
$ F_{n}=F_{n-1}+F_{n-2} $
$ F_{0}=1, F_{1}=1 $
Normally, this is considered an homogeneous second order recurrence. In order to get to a general solution, you need to write down the characteristic polynomial and get the roots (in this case, it's the golden ratio). You can find a good reference on the book by Ralph Grimaldi (chapter 7 if I'm not wrong).
Algorithmically, you just do the computations. It takes time, since you actually are computing a few numbers on repeated times (it's a typical example on topics like Dynamic Programming).
