There is no $n$; you want to find $\lim\limits_{x\to\infty}(1+x)^{1/x}$. This is a so-called $\infty^0$ indeterminate form, and there is a standard technique for computing such limits.
Let $L=\lim_{x\to\infty}(1+x)^{1/x}\;,$ and take logarithms to get $\ln L=\ln\lim_{x\to\infty}(1+x)^{1/x}=\lim_{x\to\infty}\ln(1+x)^{1/x}=\lim_{x\to\infty}\frac1x\ln(1+x)=\lim_{x\to\infty}\frac{\ln(1+x)}x\;,$ where the second equality is true because the logarithm is a continuous function. This last limit is an $\frac{\infty}{\infty}$ form, so you can use l'Hospital's rule to evaluate it. Once you have $\ln L$, remember that $L=e^{\ln L}$.