I can do the first bit, which is just manipulation of the LHS, but I'm not sure how to start on the second and third bit.
Say we wish to estimate the square rot of 2. We begin with a good first estimate , say . In fact, it is a little too big. We note that 2/1.5 is a little too small, so we form a new guess by averaging them, . We continue this method to give a sequence:
To ease notation, we set , so,
i) Show that
ii) show that
iii) How big do we require so that is within of . Find the fraction