On the interval 0 to 1 vertical lines are drawn
at the points
where k is an
odd positive integer. The height of the lines at
0 and 1 are 1 unit, the height of the line at
x=1/2 is 1/2 unit, the height
of the line at x=1/4 and x=3/4
is 1/4 unit and the height of the line
at
is
for all
values of k.
Now consider the line y=h where
. How many of the vertical
lines from x=0 to x=1 does it cut?
What happens to the heights of these lines as n
gets larger? What happens to the number of lines
cut as n gets larger?