Question

Vreau doar suma de siruri de numere. atat! VA ROG SA MA AJUTATI. dau 29 de puncte

Answer 1

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