S = - (2011 + 2013 + 2015 + ... + 2551) + (2012 + 2014 + 2016 + ... + 2554)
S = - (2011 + 2013 + 2015 + ... + 2551) + (2012 + 2014 + 2016 + ... + 2554)
= - 2011 - 2013 - 2015 - ... - 2551 + 2012 + 2014 + 2016 + ... + 2554
= (2012 - 2011) + (2014 - 2013) + ... + (2552 - 2551) + 2554
= 1 + 1 + ... + 1 + 2554
= 1 . 271 + 2554
= 271 + 2554
= 2825