I have a question #10

Question

anonymous · Answer

define $$f:I \rightarrow R$$ satisfied with$$f(x)=\frac{1+f(x-1)}{1-f(x-1)}$$ for all $$x \in I$$ 
where  $$f(1)=3$$

find $$f(2548)+f(2549)$$

mr.math · Answer

What's $I$?

asnaseer · Answer

Integers

anonymous · Answer

right

jamesj · Answer

(not standard notation, but ok ;-) )

anonymous · Answer

it is, isn't it LOL

anonymous · Answer

$$\mathbb Z$$?

jamesj · Answer

correct me if I haven't had enough coffee, but don't we have
f(1) = 3
f(2) = -2
f(3) = -1/3
f(4) = 1/2
f(5) = 3

So now f(2548) = f(4n) = f(4) = 1/2 
and f(4n+1) = f(1) = 3

mr.math · Answer

I hate you James!

asnaseer · Answer

ah - I see the pattern now James - nice solution

mr.math · Answer

I saw it, but he was faster!

asnaseer · Answer

Jesse James was always faster - wasn't he? :-)

mr.math · Answer

Yeah, that's why I hate him! :D

anonymous · Answer

lol

anonymous · Answer

i made it all the way up to f(3) and i have had 3 cups of coffee!

anonymous · Answer

he's totally right. so the ans is 7/2

anonymous · Answer

I dunno why you thought that this problem is a hard one,this type of trivial functional equations needs nothing more than some elementary induction ;)

mr.math · Answer

It's not hard at all, it's very easy actually.

anonymous · Answer

one "very" is not enough :P

anonymous · Answer

yeah - but i was  so slow seeing it - I must drink some coffee!!

anonymous · Answer

post it foolformath, the chat is quite slow