Question

-1-3-5-7-9-11-13-15-...-2015-2017​

Answer 1

 

$\displaystyle\bf\\-1-3-5-7-9-11-13-15-...-2015-2017=\\\\=-(1+3+5+7+9+...+2015+2017)\\\\In~paranteza~aplican~Formula~lui~Gauss:\\\\Canculam~numarul~de~termeni~n:\\\\n=\frac{2017-1}{2}+1=\frac{2016}{2}+1 =1008+1=1009~termeni\\\\S=-(1+3+5+7+9+...+2015+2017)=\\\\=-\frac{n(2017+1)}{2}=-\frac{1009\times 2018}{2}=-1009\times1009=-1009^2\\\\ S=-1009^2=-1018081$