Suppose 0 < a < b. Which of the following continued fractions is bigger and why?

1
2+ 1
3+ 1
a

or

1
2+ 1
3+ 1
b

Suppose the fractions are continued in the same way, then which is the bigger in the following pair and why?

1
2+ 1
3+ 1
4+[1/(a)]

or the same thing with b in place of a.

Now compare:

1
2 + 1
3+ 1
4 + ... + 1
99+ 1
100 + [1/( a)]

and the same thing with b in place of a.