Question 33
1. Compare $A$ to $0$, where:
$$
a)\ A = 1 - 2 - 3 + 4 + 5 - 6 - 7 + 8 + 9 - 10 - 11 + \dots + 2012 + 2013 - 2014 - 2015 + 2016;
$$
$$
b)\ A = \frac{1}{1} - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} - \frac{1}{7} + \frac{1}{8} + \frac{1}{9} - \frac{1}{10} - \frac{1}{11} + \dots + \frac{1}{2012} + \frac{1}{2013} - \frac{1}{2014} - \frac{1}{2015} + \frac{1}{2016}.
$$
In each question, the signs go as follows: "+" before the first term, then two "-" and two "+" signs in turn, and, finally, a "+" sign before the last term.
$$
a)\ A = 1 - 2 - 3 + 4 + 5 - 6 - 7 + 8 + 9 - 10 - 11 + \dots + 2012 + 2013 - 2014 - 2015 + 2016;
$$
$$
b)\ A = \frac{1}{1} - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} - \frac{1}{7} + \frac{1}{8} + \frac{1}{9} - \frac{1}{10} - \frac{1}{11} + \dots + \frac{1}{2012} + \frac{1}{2013} - \frac{1}{2014} - \frac{1}{2015} + \frac{1}{2016}.
$$
In each question, the signs go as follows: "+" before the first term, then two "-" and two "+" signs in turn, and, finally, a "+" sign before the last term.