$1-\frac{1}{n} \lt x \le 3 + \frac{1}{n}$, $\forall n \in \mathbb{N}$. what is the range of $x$. $1-\frac{1}{n} \lt x \le 3 + \frac{1}{n}$, $\forall n \in \mathbb{N}$. what is the range of $x$.
NOTE: $1-\frac{1}{n} \lt 3 + \frac{1}{n}$

when $n=1$,
$1-\frac{1}{n}=0$, $3+\frac{1}{n}=4$
when $n=1$, we have, $0 \lt x_{1} \le 4$
when $n=2$, we have, $\frac{1}{2} \lt x_{2} \le 3+\frac{1}{2}$
when $n \to \infty, \frac{1}{n} \to 0$, and then we have, $1 \lt x_{\infty} \le 3$
we can now conclude that, $0 \lt x \le 4$
