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Arătați ca numărul A=2021+2×(1+2+3+...+2020) este pătrat perfect

Răspuns :

A=2021+2×(1+2+3+...+2020)
A=2021+2×(2020×2021):2
A=2021+2020×2021
A=2021×(1+2020)
A=2021×2021
A=2021²
A=2021+2×(1+2+3+...+2020) =2021(2020*2021:2)=2021+2020+2021=2021(2020+1)=2021*2021=2021²⇒patrat perfect