Chapter 1.4, Problem 3P

For the following series, write formulas for the sequences a_n, S_n, and R_n, and find the limits of the sequence as $n\to \infty$ (if the limits exist).

$1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}\mathrm{...}$