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For a given M value, what are the possible N values for the limit \lim_{...

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For a given M value, what are the possible N values for the limit $\lim_{n\to\infty}\frac{n^2-1}{n+1}=\infty$ \lim_{n\to\infty}\frac{n^2-1}{n+1}=\infty?.

Note that Iff $\forall M\in \mathbb{R}^+\exists N\in \mathbb{Z}^+\forall n\in \mathbb{Z}^+,n>N\Rightarrow u_n>M$ \forall M\in \mathbb{R}^+\exists N\in \mathbb{Z}^+\forall n\in \mathbb{Z}^+,n>N\Rightarrow u_n>M then $\lim_{n\to \infty}u_n=\infty$ \lim_{n\to \infty}u_n=\infty.