e^{\lim_{n\to \infty } n\frac{n-\sqrt{n^2+ 2n}}{n+\sqrt{n^2+ 2n}}}=e^{\lim_{n\to \infty } n\frac{n-\sqrt{n^2+ 2n}}{n+\sqrt{n^2+ 2n}}\frac{n+\sqrt{n^2+ 2n}}{n+\sqrt{n^2+ 2n}}}=e^{\lim_{n\to \infty } n\frac{-2n}{\left(n+\sqrt{n^2+ 2n}\right)^2}}=e^{\lim_{n\to \infty } \frac{-2n^2}{n^2+2n\sqrt{n^2+ 2n}+n^2+2n}}=