## Calculus: Early Transcendentals (2nd Edition)

First four terms: $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$ Sum: $S_\infty = 2$
The next term is the previous term multiplied by a factor of $\frac{1}{2}$. The first four terms are given in the problem: $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$ The infinite series is a geometric sequence with the an initial term of $a_0 = 1$ and a factor of $r = \frac{1}{2}$, where $r<1$. $S_\infty = \frac{a_0}{1-r} = \frac{1}{1- \frac{1}{2}} = 2$