Giải thích các bước giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\begin{array}{l}
\dfrac{{{a_1}}}{{{a_2}}} = \dfrac{{{a_2}}}{{{a_3}}} = \dfrac{{{a_3}}}{{{a_4}}} = .... = \dfrac{{{a_{2017}}}}{{{a_{2018}}}} = \dfrac{{{a_1} + {a_2} + {a_3} + {a_4} + .... + {a_{2017}}}}{{{a_2} + {a_3} + {a_4} + ..... + {a_{2018}}}}\\
\Rightarrow {\left( {\dfrac{{{a_1}}}{{{a_2}}}} \right)^{2017}} = {\left( {\dfrac{{{a_1} + {a_2} + {a_3} + {a_4} + .... + {a_{2017}}}}{{{a_2} + {a_3} + {a_4} + ..... + {a_{2018}}}}} \right)^{2017}}\\
{\left( {\dfrac{{{a_1}}}{{{a_2}}}} \right)^{2017}} = \dfrac{{{a_1}}}{{{a_2}}}.\dfrac{{{a_1}}}{{{a_2}}}.\dfrac{{{a_1}}}{{{a_2}}}.....\dfrac{{{a_1}}}{{{a_2}}}\,\,\,\,\,\,\,\,\,\,\,\,\left( {2017\,\,t/s\,\,\,\dfrac{{{a_1}}}{{{a_2}}}} \right)\\
= \dfrac{{{a_1}}}{{{a_2}}}.\dfrac{{{a_2}}}{{{a_3}}}.\dfrac{{{a_3}}}{{{a_4}}}......\dfrac{{{a_{2017}}}}{{{a_{2018}}}}\\
= \dfrac{{{a_1}}}{{{a_{2018}}}}\\
\Rightarrow \dfrac{{{a_1}}}{{{a_{2018}}}} = {\left( {\dfrac{{{a_1} + {a_2} + {a_3} + {a_4} + .... + {a_{2017}}}}{{{a_2} + {a_3} + {a_4} + ..... + {a_{2018}}}}} \right)^{2017}}
\end{array}\)
