Tony Cardell, age 14, State College Area High School, Pennsylvania, USA and Chi Kin Ho, age 17, Saint Dominic's International School, Lisbon sent in excellent solutions and here is Chi Kin's:

What happens when successive terms are taken in the continued fraction

I calculated the first five terms

Thus, when successive terms are taken, the results oscillate alternately above and below 3.

Indeed, if the fraction goes on forever, we would get 3.

Suppose the continued fraction is denoted as F . Thus

Thus F = 3, because F cannot be negative.