Chapter 11 - Section 11.3 - Series - Exercise Set - Page 651: 32

$ 1 $

The first 7 terms of $ a_n=(-1)^{n-1} $ are \begin{array}{l} a_1=(-1)^{1-1}\\ a_1=(-1)^{0}\\ a_1=1 ,\\\\ a_2=(-1)^{2-1}\\ a_2=(-1)^{1}\\ a_2=-1 ,\\\\ a_3=(-1)^{3-1}\\ a_3=(-1)^{2}\\ a_3=1 ,\\\\ a_4=(-1)^{4-1}\\ a_4=(-1)^{3}\\ a_4=-1 ,\\\\ a_5=(-1)^{5-1}\\ a_5=(-1)^{4}\\ a_5=1 ,\\\\ a_6=(-1)^{6-1}\\ a_6=(-1)^{5}\\ a_6=-1 ,\\\\ a_7=(-1)^{7-1}\\ a_7=(-1)^{6}\\ a_7=1 .\end{array} Hence, the partial sum is $ 1-1+1-1+1-1+1= 1 $.