(2017 年全国普通高等学校招生统一考试数学（浙江卷精编版 ）已知数列 {xn}\left\{ {x}_{n}\right\}{xn} 满足: x1=1{x}_{1} = 1x1=1 ,xn=xn+1+ln(1+xn+1)(n∈N∗){x}_{n} = {x}_{n + 1} + \ln \left( {1 + {x}_{n + 1}}\right) \left( {n \in {N}^{ * }}\right)xn=xn+1+ln(1+xn+1)(n∈N∗)证明: 当 n∈N∗n \in {N}^{ * }n∈N∗ 时,(1) 0<xn+1<xn0 < {x}_{n + 1} < {x}_{n}0<xn+1<xn ;(2) 2xn+1−xn≤xnxn+122{x}_{n + 1} - {x}_{n} \leq \frac{{x}_{n}{x}_{n + 1}}{2}2xn+1−xn≤2xnxn+1 ;(3) 12n−1≤xn≤12n−2\frac{1}{{2}^{n - 1}} \leq {x}_{n} \leq \frac{1}{{2}^{n - 2}}2n−11≤xn≤2n−21 .