Check if $a_n=(n-1)/(n+1)$ is bounded

Question

It seems that $n\geq 0$ but I can't get a bound out of this. This sequence is increasing so $a_n \geq a_0=-1$ if I understand correctly but for it to be bounded don't we need an upper bound also?

Answer 1

Let $n \in \mathbb{N}:$

$-1\le \dfrac{n-1}{n+1} =1 -\dfrac{2}{n+1} \lt 1.$

Answer 2

Because $n-1<n+1$ for every integer $n$, we must have (for $n > -1$): $$\frac{n-1}{n+1}<1$$