2×(1+2+3+...+2019)+2020 =
= 2×2019×2020 : 2 + 2020
= 2019×2020 + 2020
= 2020(2019 + 1)
= 2020×2020
= 2020²
Suma lui Gauss: 1+2+3+...+n=[n*(n+1)]/2
1+2+3+...+2019=2019*(2019+1)/2=2019*2020/2
2*(1+2+3+...+2019)=
=2*2019*2020/2+2020
2 de la numărător se simplifică cu 2 de la numitor
=2019*2020+2020
2020 e factor comun
=2020(2019*1+1)
=2020*(2019+1)
=2020*2020
=2020^2=>pătrat perfect
