Prove Using Definition that the Sequence $\frac{n+1}{\sqrt{n}+2}$ Diverges to Infinity Formally, a sequence $x_n$ diverges to infinity whenever for all $M>0$ there exists $N(M)$ such that $n>N(M)$ implies $x_n>M$.
Prove formally, using the definition, that the following sequence diverges to infinity:
\begin{equation}
x_n=\frac{n+1}{\sqrt{n}+2}
\end{equation}
Proof. Let $M>0$. Take $N(M)=?$...

Hints: 
$$x_n\ge \frac{n-4}{\sqrt{n}+2}=\sqrt{n}-2 > M$$
Can you proceed from here?
