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R=2016+2x(1+2+3+....+2015) este pătrat pefect?

Răspuns :

1+2+...+2015=(2015×2016)/2

R=2016+2×(2015×2016)/2=

2016+2015×2016=2016 (1+2015)=

2016×2016=2016^2
Progresie aritmetica
R=2016+2 x (1+2015) x 2015 :2 =2016(1+2015)=2016^2, deci patrat perfect al lui 2016.