8.
已知数列\(\left\{ {{a}_{n}} \right\}\),\({{a}_{n}} > 0\),其前\(n\)项和\({{S}_{n}}\)满足\({{S}_{n}}=2{{a}_{n}}-{{2}^{n+1}}\),其中\(n\in N*\).
\((\)Ⅰ\()\)设\({{b}_{n}}=\dfrac{{{a}_{n}}}{{{2}^{n}}}\),证明:数列\(\left\{ {{b}_{n}} \right\}\)是等差数列;
\((\)Ⅱ\()\)设\({{c}_{n}}={{b}_{n}}\cdot {{2}^{-n}}\),\({{T}_{n}}\)为数列\(\left\{ {{c}_{n}} \right\}\)的前\(n\)项和,求证:\({{T}_{n}} < 3\);
\((\)Ⅲ\()\)设\({{d}_{n}}={{4}^{n}}+{{(-1)}^{n-1}}\lambda \cdot {{2}^{{{b}_{n}}}}(\lambda \)为非零整数,\(n\in N*)\),试确定\(\lambda \)的值,使得对任意\(n\in N*\),都有\({{d}_{n+1}} > {{d}_{n}}\)成立.