What is $\lim _{ x\to { 1 }^{ - } }{ \prod _{ n=0 }^{ \infty }{ { \left( \frac { 1+{ x }^{ n+1 } }{ 1+{ x }^{ n } } \right) }^{ { x }^{ n } } } }$?
Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$