已知正整数\(a_1,a_2,\cdots ,a_{2016}\)成等比数列,公比\(q\in (1,2)\),则\(a_{2016}\) 取最小值时,\(q=\)______ 解答: 显然\(q\)为有理数,令\(q=\dfrac{m}{n},m\in N^+,n\in N^+,(m,n)=1\) 设数列\(a_1,a_2,\cdots ,a_{2016}\)为\[n^{2015}a,n^{2014}ma,\cdots ,m^{2015}a,\] 由于\(q\in(1,2)\)得\(n<m<…