Chapter 11 - Section 11.3 - Series - Exercise Set - Page 651: 31

$0$

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