$ N = 1 - 5 - 9 + 13 + 17 - 21 - 25 + 29 + ... + 2001 - 2005 - 2009 + 2013 \\ = (1 - 5) + (- 9 + 13) + (17 - 21) + (-25 + 29) + ... (2001 - 2005) + (-2009 + 2013) \\ = (-4) + 4 + (-4) + 4 + ... (-4) + 4 \\ = 0 + 0 + ... + 0 \\ = 0 $
$ P = \frac{2010}{2011} + \frac{2011}{2012} + \frac{2012}{2013} > \frac{2010}{2011 + 2012 + 2013} + \frac{2011}{2011 + 2012 + 2013} + \frac{2012}{2011 + 2012 + 2013} = \frac{2010 + 2011 + 2012}{2011 + 2012 + 2013} = Q $
$ B = 1 . 2 . 3 . ... . 2012\left (1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{2012} \right ) \\
= 1 . 2 . 3 . ... . 671. ... . 2012\left (1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{2012} \right ) \\ = (3 . 671) . 1 . 2 . 4 . ... . 2012\left (1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{2012} \right ) \\ = 2013 . 1 . 2 . 4 . ... . 2012\left (1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{2012} \right ) \vdots 2013 $