Question

aratati ca numarul 2015+2•(1+2+3+…+2014) este patrat perfect. Va rog

Answer 1

Răspuns:

2015 + 2 • (1+2+3+…+2014) =

2015 + 2 × 2014 × 2015 : 2 =

2015 + 2014 × 2015 =

2015 × (1 + 2014) =

2015 × 2015 =

2015² ⇒ patrat perfect

Answer 2

$\it 2015+2\cdot(1+2+3+\ ...+2014)=2015+\not2\cdot\dfrac{2014\cdot2015}{\not2}=\\ \\ \\ =2015+2014\cdot2015=2015(1+2014)=2015\cdot2015=2015^2$