Let f(x) = 1 x+1 . Let fn (x) to be the function f composed with itself n times. (For example, f3 (x) = f(f(f(x))).) Using trial and error, conjecture a guess for f n(x) and use mathematical induction to prove that guess. Your guess should be a closed form without any summations in it. The constants/variables that should appear in your guess n and x.