2 × ( 1 + 2 + 3 + ...... + 2018 ) + 2019 =
= 2 × 2018 × ( 1 + 2018 ) : 2 + 2019
= 2018 × 2019 + 2019 =
= 2019 × ( 2018 + 1 ) =
= 2019 × 2019 =
= 2019² → patrat perfect
_______________________
1 + 2 + 3 + .... + 2018 =→ aplic formula sumei lui Gauss
= 2018 termeni × [ 1 ( primul termen) + 2018 ( ultimul termen al sumei ) ] : 2
