So, ,
(
Actually, by induction you can prove that for every natural ,
I did not have an issue with the topic when it was relatively straight forward in that it gave f(0) and then wanted f(1),f(2),f(3)....
The problem arose when they gave f(0) and f(1) and wanted f(2),f(3),f(4),f(5)...
I'm going to pick a non homework portion of the problem:
Find f(2),f(3),f(4),F(5) if f is defined recursively by f(0)=f(1)=1 and for n=1,2,..
With f(n+1)=f(n)f(n-1)
Thanks for any help.
Thanks, I guess it probably really didn't help me understand the process with f(0) and f(1) both = 1. What if like f(0)=2 and f(1)=3? Which is where I am mixed up, attempting to determine the relationship betweeen f(0) and f(1) in determing the remaining functions. Thanks though, your reply gave me some insight, I'm just trying to figure out how to work with these two together. like f(2)=5=5(5-1)=20 f(3)=(21+1)=22(22-21)...? If you were to run through your process through these, or smaller (if others too high) I feel certain I would understand completely. Thanks.
Not really sure of the wording. But f(n) will always be 1 in this case. Not sure if that is what you are asking. Or is it something else? LOL Gimme a hint on it, I'm holding on to the seat of my pants here. On one hand I love the course, haven't had to think this hard in years, on the other I'm not sure I've disliked a course at much at the same time either. (Protective of GPA).
Basis step: p(1)....f(n+1)=f(n)-f(n-1)=1=f(1)-f(1-1)=1-0=1.....1=1
Inductinve step: 1+2+..+(k+1)-(k+1-1)
k(2)=k+1-k=1.
k(3)=k+1-k=1.....
Really not so sure I did that right, although I did establish the formula always came back as 1, I'm confused because I thought the 1+2+....had to be added, and that does not balance. Feel free to point me in the right direction.