Áp dụng tính chất dãy tỉ số bằng nhau ta có:
$\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{a}_{2}}}{{{a}_{3}}}=\frac{{{a}_{3}}}{{{a}_{4}}}=...=\frac{{{a}_{2014}}}{{{a}_{2015}}}=\frac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+...+{{a}_{2014}}}{{{a}_{2}}+{{a}_{3}}+{{a}_{4}}+...+{{a}_{2015}}}$
Khi đó $\frac{{{a}_{1}}}{{{a}_{2}}}.\frac{{{a}_{2}}}{{{a}_{3}}}.\frac{{{a}_{3}}}{{{a}_{4}}}.....\frac{{{a}_{2014}}}{{{a}_{2015}}}={{\left( \frac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+...+{{a}_{2014}}}{{{a}_{2}}+{{a}_{3}}+{{a}_{4}}+...+{{a}_{2015}}} \right)}^{2014}}$
.hay $\frac{{{a}_{1}}}{{{a}_{2015}}}={{\left( \frac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+...+{{a}_{2014}}}{{{a}_{2}}+{{a}_{3}}+{{a}_{4}}+...+{{a}_{2015}}} \right)}^{2014}}$