[tex] \lim_{n \to \infty} n- \sqrt{ n^{2} +4n+5}= \lim_{n \to \infty} \frac{ n^{2}- n^{2}-4n-5 }{n+ \sqrt{n^{2}+4n+5} }[/tex]
[tex]== \lim_{n \to \infty} \frac{n(-4- \frac{5}{n} )}{n(1+ \sqrt{1+ \frac{4}{n}+ \frac{5}{n^{2}} } )}= - \frac{4}{2}=-2 [/tex]
