Question

simplest form of 2016 square - 2015 square + 2014 square - 2013 2012 and so on 2 square minus 1 square is

Answer 1

This is basically:
-1²+2²-3²+4²+..-2015²+2016²
(2+1)(2-1) + (4+3)(4-3) + (6+5)(6-5)+.. (2016+2015)(2016-2015)
= 3+7+11+15+....+4031
We get an AP with a=3 , l=4031 , n = 2016/2= 1008
Sum = (1008/2)(3+4031) = 2,033,136