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安徽省2023-2024年下学期八年级卷二数学.考卷答案试卷答案
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分析利用等比数列的求和公式，化简，再代入计算，即可得出结论．
解答解：∵$\frac{{{S_{504}}}}{{{S_{1008}}}}$=$\frac{1}{10}$，
∴$\frac{\frac{{a}_{1}（1-{q}^{504}）}{1-q}}{\frac{{a}_{1}（1-{q}^{1008}）}{1-q}}$=$\frac{1}{10}$，
∴$\frac{1}{1+{q}^{504}}$=$\frac{1}{10}$，
∴q504=9，
∴$\frac{{{S_{1008}}}}{{{S_{2016}}}}$=$\frac{1}{1+{q}^{1008}}$=$\frac{1}{82}$．
故选：B．
点评本题考查等比数列的求和公式，考查学生的计算能力，属于中档题．
