# Find the sum of the following series $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots + \infty$

$(a)\;2\qquad(b)\;3\qquad(c)\;\frac{3}{2}\qquad(d)\;\infty$

Toolbox:
• Sum of n terms of a GP is $S_{\infty} = \large \frac{a} {1 - r}$ when $r < 1$
Sum of n terms of a GP is $S_{\infty} = \large \frac{a} {1 - r}$ when $r < 1$
Here, $a = 1, r = \frac {1}{2}$
$S_{\infty} = \Large\frac {1}{1 - \frac{1}{2}}$$= 2$
edited Jul 2, 2014