Răspuns:
-1009
Explicație pas cu pas:
1+3+5+......+2015+2017-2-4-6-.....-2016-2018 =
= (1-2)+(3-4)+(5-6)+.....+(2015-2016)+(2017-2018) = (-1)·1009 = -1009
Primul sir de numere are : (2017-1):2+1 termeni = 1009 termeni
Al doilea sir are : (2018-2):2+1 = 1009 termeni
Varianta II (folosind formula lui Gauss) :
1+3+5+......+2015+2017 = (1+2017)·[(2017-1):2+1 ]:2 = 2008·1009:2 =
= 1009·1009 = 1009²
-2-4-6-.....-2016-2018 = (-2)·(1+2+3+4+.....+1009) =
= (-2)·(1+1009)·1009:2 = (-1)·1010·1009 =>
1+3+5+......+2015+2017-2-4-6-.....-2016-2018 =
=1009·1009-1009·1010 = 1009·(1009-1010) = 1009·(-1) = -1009
