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Aratati ca numarul a = 2017 +2•(1+2+....+2016) edte patrat perfect

Răspuns :

a = 2017 + 2(1 + 2 + .. + 2016)

= 2017 + 2×2016×2017 : 2

= 2017 + 2016×2017

= 2017(1 + 2016)

= 2017×2017

= 2017²

Răspuns:

Explicație pas cu pas:

a = 2017 + 2 × ( 1 + 2 + ...... + 2016 )

a = 2017 + 2 × 2016 × (1 + 2016 ) : 2

a = 2017 + 2016 × 2017

a = 2017 × ( 1 + 2016 )

a = 2017 × 2017

a = 2017² → patrat perfect