Question

Lt (1/n)^(1/ln n)=?
n->infty

Answer 1

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