Man Vs Wild Summations!

If

$\large\ \lim _{ x\rightarrow { 1 }^{ - } }{ \prod _{ n=0 }^{ \infty }{ { \left( \frac { 1 + { x }^{ n+1 } }{ 1 + { x }^{ n } } \right) }^{ { x }^{ n } } } } = l$ .

Then find the integral part of the number $\frac { 1 }{ l }$ .