已知数列\(\{a_{n}\}\)满足：\(a_{1}=1\)，\(3a \;_{ n+1 }^{ 2 }+3a \;_{ n }^{ 2 }-10a_{n}a_{n+1}=3\)，\(a_{n} < a_{n+1}(n∈N^{+}).\)
\((\)Ⅰ\()\)证明：\(\{3a_{n+1}-a_{n}\}\)是等比数列；
\((\)Ⅱ\()\)设数列\(\{a_{n}\}\)的前\(n\)项和为\(S_{n}\)，求证：\( \dfrac {n^{2}}{S_{n}}\leqslant \dfrac {1}{a_{1}}+ \dfrac {1}{a_{2}}+…+ \dfrac {1}{a_{n}} < \dfrac {3}{2}\)．

【考点】数列的综合应用,等比数列的判定与证明

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