Let a = sqrt(3) -1. prove that
a = 1/(1 + 1/(2 + a) )
Use this to find the continued fraction expansion for a.
Deduce the continued fraction expansion for sqrt(3).
Check that your answer makes sense - that is , use the first 6 or 7 terms of the continued fraction expansion to give an approximation for sqrt(3) and make sure that this approximation is reasonable.
Can you teach me how to solve this question? Thank you very much.