Răspuns :
Răspuns:
Explicație pas cu pas:
2 + 4 + 6 + ...+ 4040
an = a1 + (n - 1)*r
a1 = 2
an = 4040
r = 2
4040 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n
n = 4040 : 2 = 2020 termeni in suma
2 + 4 + 6 + ...+ 4040 = 2020*(2 + 4040)/2 = 2020*4042/2 = 2020*2021
a = 2020*2021 - 2020 = 2020*(2021 - 1) = 2020*2020 = 2020^2 patrat perfect
a=(2+4+6+...+4040)-2020
a=2×(1+2+3+...+2020)-2020
a=2×(2020×2021)/2-2020
a=2020×2021-2020
a=2020×(2021-1)
a=2020×2020
a=2020²⇒ a este patrat perfect