Chapter 11 - Infinite Sequences and Series - 11.2 Series - 11.2 Exercises - Page 758: 81

The step $=1+(-1+1)+(-1+1)+(-1+1)+...$ is incorrect since addition is only associative for finitely many terms, not for infinitely many terms.

$0=0+0+0+...$ $=(1-1)+(1-1)+(1-1)+(1-1)+...$ $=1-1+1-1+1-1+...$ $=1+(-1+1)+(-1+1)+(-1+1)+ ...$ Step: (1) $=1+0+0+0...=1$ Hence, the step (1) that is, $=1+(-1+1)+(-1+1)+(-1+1)+...$ is incorrect since addition is only associative for finitely many terms, not for infinitely many terms.