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ex5: aratati ca numarul 2.015+2x(1+2+3+.....+2.014) este patrat perfect .

Răspuns :

1 + 2 + 3 + ... + 2014 = 2014 x 2015 /2 = 1007 x 2015
2015 + 2 x 1007 x 2015 = 2015 + 2014 x 2015 = 2015( 1 = 2014) = 2015 x 2015 = 2015² deci patrat perfect