Question

(+1)+(-2)+(+3)+(-4)+(+5)+(-6)+...+(-2018)

Answer 1

$( + 1) + ( - 2) + ( + 3) + ( - 4) + ( + 5) + ( - 6) + ... + ( - 2018)$

$= 1 - 2 + 3 - 4 + 5 - 6 + ... + 2017 - 2018$

$= 1 + 3 + 5 + ... + 2017 - 2 - 4 - 6 -8- ... - 2018$

$1+3+5+...+2017$

$1+3+5+...+2n-1={n}^{2}$

$2n-1=2017$

$2n=2017+1$

$2n=2018\:|\:\div2$

$n=1009$

${n}^{2}={1009}^{2}$

$= {1009}^{2} - 2(1 + 2 + 3 + 4+... + 1009)$

$= {1009}^{2} - 2 \times \frac{1009(1009 + 1)}{2}$

$= {1009}^{2}- 1009 \times 1010$

$= 1009(1009 - 1010)$

$= 1009 \times (-1)$

$= -1009$