Chapter 11 - Review Exercises - Page 841: 51

$\displaystyle \sum_{i=1}^{7}2^{i-1}=127$

$\displaystyle \sum_{i=1}^{7}2^{i-1}=2^0+2^1+...+2^6$ $a_1=2^0=1$ $r=\frac{a_2}{a_1}=\frac{2^1}{2^0}=2$ $S_n=a_1(\frac{1-r^n}{1-r})$ $S_7=1(\frac{1-2^7}{1-2})=\frac{1-128}{-1}=127$