\( 8 + 4 + 2 + 1 + \ldots + \frac { 1 } { 16 } \)

This sequence is a geometric series where each term is half of the previous one, starting from 8. To find the sum, we can use the formula for the sum of a geometric series: \( S_n = a \frac{1 - r^n}{1 - r} \), where \( a \) is the first term, \( r \) is the common ratio, and \( n \) is the number of terms. Here, \( a = 8 \), \( r = \frac{1}{2} \), and we can see that the series continues until it reaches \( \frac{1}{16} \). This series actually has 5 terms: \( 8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16} \). You can calculate the sum step by step: \[ 8 + 4 = 12 \] \[ 12 + 2 = 14 \] \[ 14 + 1 = 15 \] \[ 15 + \frac{1}{2} = 15.5 \] \[ 15.5 + \frac{1}{4} = 15.75 \] \[ 15.75 + \frac{1}{8} = 15.875 \] \[ 15.875 + \frac{1}{16} = 15.9375 \] Ultimately, the sum of the series is \( 15.9375 \) or you can express it as \( 15 \frac{15}{16} \).