[tex]\it E(x) =\dfrac{|x|}{x},\ \ x\in\mathbb{Z}^*\\ \\ a)\ \ E(-1)=\dfrac{|-1|}{-1}=\dfrac{1}{-1}=-1\\ \\ E(1)=\dfrac{|1|}{1}=\dfrac{1}{1}=1\\ \\ \\ b)\ \ E(-n)+E(n)=\dfrac{|-n|}{-n}+\dfrac{|n|}{n} =-\dfrac{|n|}{n}+\dfrac{|n|}{n}=\dfrac{-|n|+|n|}{n}=\dfrac{0}{n}=0[/tex]
c) Se poate observa că:
[tex]\it \forall n\in\mathbb{N}^*\Longrightarrow\begin{cases}\it E(n)=\dfrac{|n|}{n}=\dfrac{n}{n}=1\\ \\ \\ \it E(-n)=\dfrac{|-n|}{-n}=\dfrac{n}{-n}=-1\end{cases}[/tex]
Suma din enunț se scrie:
[tex]\it \underbrace{(1-1)+(1-1)+(1-1)+\ ...\ +(1-1)}_{50\ paranteze}=0[/tex]
