Evaluating $\lim_{x\to 1^{-}} \prod_{n=0}^{\infty} \left (\frac{1+x^{n+1}}{1+x^n}\right)^{x^n}$
Finding $\lim\limits_{x\to1^-}\Bigl(\prod\limits_{n=0}^{\infty}\Bigl(\frac{1+x^{n+1}}{1+x^n}\Bigr)^{x^n}\Bigr)$