题型:解答题 题类:其他 难易度:较易
已知单调的等比数列\(\{{{a}_{n}}\}\)的前\(n\)项和为\({{S}_{n}}\),若\({{S}_{{3}}}=39\),且\(3{{a}_{4}}\)是\({{a}_{6}}\),\(-{{a}_{5}}\)的等差中项.
\((\)Ⅰ\()\)求数列\(\{{{a}_{n}}\}\)的通项公式;
\((\)Ⅱ\()\)若数列\(\{{{b}_{n}}\}\)满足\({{b}_{n}}={{\log }_{3}}{{a}_{2n-1}}\),且\(\{{{b}_{n}}\}\)前\(n\)项的和为\({{T}_{n}}\),求\(\sum\limits_{i=1}^{n}{\dfrac{1}{{{T}_{i}}}} < 2\).