The infinite series 1/2 + 1/4 + 1/8 + 1/16 ... is not equal to 1.

The series will always follow an x-1/x form

1/2
1/2 + 1/4
3/4
3/4 + 1/8
7/8
7/8 + 1/16
15/16
...
and so on.

It will remain in the form x-1/x, instead of the x/x that is one.

jman_red