\(2016-1+2-3+4-...-2015\)
\(=2016-\left(1-2+3-4+...+2015\right)\)
\(=2016-\left[\left(1-2\right)+\left(3-4\right)+...+\left(2013-2014\right)+2015\right]\)
\(=2016-\left(-1+\left(-1\right)+...+\left(-1\right)+2015\right)\)
\(=2016+\left(1+1+1+...+1-2015\right)\)
\(=2016+\left(2014-2015\right)\)
\(=2016+\left(-1\right)\)
\(=2015\)
2016 - 1 + 2 - 3 + 4 - ... - 2015
= (2016 + 2 + 4 + .. + 2014) - (1 + 3 + 5 + ... + 2015)
= \(\dfrac{\left(2016-4\right):2+1}{2}\times\left(2+2016\right)-\dfrac{\left(2015-1\right):2+1}{2}\times\left(1+2015\right)\)
= 1016063 - 1016064
= -1
