共50条信息
若二项式\({\left(x- \dfrac{a}{ \sqrt[3]{x}}\right)}^{6} \)展开式中含\({x}^{2} \)项的系数为\( \dfrac{5}{2} \)，则\( \lim\limits_{n→∞}\left(1+a+{a}^{2}+⋯+{a}^{n}\right) =\)_______．
已知数列\(\left\{{a}_{n}\right\} \)中，\({a}_{1}=1,{a}_{n+1}+{a}_{n}={\left( \dfrac{1}{3}\right)}^{n}(n∈{N}^{*}) \)，则\( \lim\limits_{n→∞}({a}_{1}+{a}_{2}+{a}_{3}+⋯+{a}_{2n-1})= \) ．
已知数列\(\left\{{a}_{n}\right\} \)是首项为\(1\)，公差为\(2\)的等差数列，，\({S}_{n} \left(n∈{N}^{*}\right) \)表示数列\(\left\{{a}_{n}\right\} \)的前\(n\)项和，则\( \lim\limits_{n→∞} \dfrac{{S}_{n}}{{n}^{2}-1}= \) ．
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