1．
已知数列\(\{x_{n}\}\)满足：\(x_{1}=1\)，\(x_{n}=x_{n+1}+\ln (1+x_{n+1})(n∈N^{*})\)，证明：当\(n∈N^{*}\)时，
\((\)Ⅰ\()0 < x_{n+1} < x_{n}\)；
\((\)Ⅱ\()2x_{n+1}-x_{n}\leqslant \dfrac {x_{n}x_{n+1}}{2}\)；
\((\)Ⅲ\() \dfrac {1}{2^{n-1}}\leqslant x_{n}\leqslant \dfrac {1}{2^{n-2}}\)．