Posted by miki on .
Given f(11)=11 and f(x+3) = (f(x)1)/(f(x)+1) for all x, find f(2000)

UMD 
Calc1,
Please don't do this. I will have to destroy your grade kiddo.
Turfe 
CALC 1 
Your friendly neighborhood classmate,
Hey, thank me in class for doing your work for you :P
Look for the pattern
f(11) = 11
f(14) = (11  1)/(11 + 1) = 10/12 = 5/6
f(17) = (5/6  1)/(5/6 + 1) = (1/6) / (11/6) = 1/11
f(20) = (1/11  1)/(1/11 + 1) = 12/11 / (10/11) = 12/10 = 6/5
f(23) = (6/5  1)/(6/5 + 1) = 11/5 / (1/5) = 11
so it repeats every 12 numbers (23  11 = 12)
and since 2000 = 165 • 12 + 20, f(2000) will be the same as f(20) = 6/5
:P