$Y=\lim_{n \rightarrow \infty} (1/n)^{1/ \ln n}$ Taking logarithm $\ln Y=\lim_{n \rightarrow \infty} (1/\ln n)\times(\ln (1/n))$ $\ln Y=\lim_{n \rightarrow \infty} (1/\ln n)\times[-\ln (n)]$ $\ln Y=\lim_{n \rightarrow \infty} (-1)$ $\ln Y=(-1)$ $Y=e^{-1}$