Răspuns:
Explicație pas cu pas:
2 × ( 1 + 2 + 3 + ... + 2018 ) + 2019 =
= 2 × 2018 × ( 1 + 2018 ) : 2 + 2019 =
= 2018 × 2019 + 2019 =
= 2019 × ( 2018 + 1 ) =
= 2019 × 2019 =
= 2019² → patrat perfect
2×(1 + 2 + 3 + .. + 2018) + 2019 =
= 2×2018×2019 : 2 + 2019
= 2018×2019 + 2019
= 2019×(2018 + 1)
= 2019×2019
= 2019²
Obs. Am folosit formula lui Gauss pentru numere consecutive :
1 + 2 + .. + n = n(n + 1) / 2
