Question

Fie dependenta functionala R - R notata y=E(x)=2*x-1
aratati ca radical din E(1)+E(2)+...+E(N) este nr natural, unde n-nenul
plz help!

Answer 1

E(1)+E(2)+E(3)+...+E(N)=1+3+5+...+(2n-1)
Fie suma expresiilor - S
$S=\dfrac{n\cdot (2n-1+1)}{2}=\dfrac{n \cdot 2n}{2}=n \cdot n=n^2\Rightarrow \sqrt{n^2}=n \in \mathbb{N}$