Write the sum in sigma notation $LaTeX: \displaystyle 8+4+2\ldots$ and then find the sum.

Taking the ratio of the first two terms gives $LaTeX: \displaystyle r = \frac{a_2}{a_1}=\frac{4}{8}=\frac{1}{2}$ . Using $LaTeX: \displaystyle a_{1}$ and $LaTeX: \displaystyle r$ to write in sigma notation gives $LaTeX: \displaystyle \sum_{n=1}^{\infty}8\left( \frac{1}{2} \right)^{n-1}$ . Using the formula for the sum of an infinite geometric series gives $LaTeX: \displaystyle \frac{8}{1-(\frac{1}{2})}=16$