# How do you use summation notation to expression the sum 2-1/2+1/8-...+1/2048?

${\sum}_{n = 0}^{6} \left[2 \cdot {\left(- \frac{1}{4}\right)}^{n}\right]$
This is a geometric sequence with a ratio of $\left(- \frac{1}{4}\right)$
The major problem is to determine the value of $n$ for which $2 \cdot {\left(- \frac{1}{4}\right)}^{n}$ is equal to $\frac{1}{2048}$. This can be done by trial and error, although it helps to remember that $1024 = {2}^{10} = {4}^{5}$