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+... ... 100+[(1)/(a)]

and the same thing with b in place of a.