A step function f(x) is defined on the interval [0, 1)

From [0, 1/2), the step is 1/2 high.
From [1/2, 3/4), the step is 3/4 high
From [3/4, 7/8), the step is 7/8 high
From [ 1 - 1/(2^k), 1 - 1/(2^(k+1)) ) the step is 1 - 1/(2^(k+1)) high

What is the exact area under the step function?

I did it in binary and got .101010... with the 10's repeating forever, or 2/3 as a common fraction.

Posted by Richard on 2004-07-07 12:23:19