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

Before you say that you should probably look up a definition of a series. (In at least a couple of messages in this thread you can find it mentioned.)

The infinite series 1/2 + 1/4 + 1/8 + 1/16 ... is equal to 1! Period.
Please do not confuse the above series with the sequence

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

First, you have to ask yourself, is whatever you have in mind while writing

1/2 + 1/4 + 1/8 + 1/16 ...

is a number or not. I suspect you think it is a number, although you have been missing its definition. As any other number, it is fixed. It has a value. What is it? You say it is less than 1. Fine. How much less? Think of that.