# DEPRECATED Interpreting the structure of expressions

### Problem

The formula for the sum of the powers of space, start fraction, 1, divided by, 2, end fraction, space from 0 to 100 is given by
$\qquad1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2\cdots+\left(\dfrac{1}{2}\right)^{100}=2-\left(\dfrac{1}{2}\right)^{100}$
Which of the following is the correct formula for
space, 1, plus, start fraction, 1, divided by, 2, end fraction, plus, start fraction, 1, divided by, 4, end fraction, plus, start fraction, 1, divided by, 8, end fraction, plus, start fraction, 1, divided by, 16, end fraction, space, question mark, space, space, space
Please choose from one of the following options.
Based on these cases, what is the sum of the powers of space, start fraction, 1, divided by, 2, end fraction, space from 0 to n ?