Question

Efectuati 1*(-1)+2*(-1)^2+...+2019*(-1)^2019

Answer 1

Răspuns:

-1010

Explicație pas cu pas:

1*(-1)+2*(-1)^2+...+2019*(-1)^2019 =

-1+2-3+4-5+ ... +2018x(-1)^2018 - 2019 =

-(1+3+5+ ... + 2019) + 2(1+2+ ... +1009) = (progresie aritmetica si suma Gauss)

-((2019-1)/2 + 1)(2019+1)/2 + 2*1009(1009+1)/2 =

-(2018/2  +  1) x 2020/2 + 1009*1010 =

- 1010 x 1010 + 1009*1010 =

1010(-1010 + 1009) =

1010 x (-1) =

-1010.