Question

1•(-1)^2+2•(-1)^3+3•(-1)^4+...+2018•(-1)^2019

Answer 1

S = 1•(-1)²+2•(-1)³+3•(-1)⁴+...+2018•(-1)²⁰¹⁹ = 1 - 2 + 3 - 4+ ... +2017 - 2018

Suma algebrică conține 2018 termeni.

Vom asocia temenii câte doi :

S = (1 - 2)+(3 - 4)+ ... +(2017-2018)

Suma are 2018:2=1009 paranteze, fiecare paranteză este egală cu -1.

S = -1·1009 = -1009

Answer 2

$S = 1\cdot (-1)^2+2\cdot (-1)^3+3\cdot (-1)^4+...+2018\cdot (-1)^{2019} \\ \\ S= 1-2+3-...-2016+2017-2018 \\ S = (1-2)+(3-4)+...+(2015-2016)+(2017-2018) \\ S = -1-1-1-\underset{de~\frac{2018}{2} = 1009~ori}{\underbrace{...}}-1\\\\S = -1\times 1009=-1009$