[Thgx0312555]

ข้อ 12

$(\dfrac{6}{5}\times\dfrac{9}{8}\times\cdots\times\dfrac{2010}{2009}\times \dfrac{2013}{2012})^3$

$ =\dfrac{6}{5}\times\dfrac{6}{5}\times\dfrac{6}{5}\times\dfrac{9}{8}\times\cdots\times\dfrac{2013}{2012}\times \dfrac{2013}{2012} \times \dfrac{2013}{2012}$

$> \dfrac{6}{5}\times\dfrac{7}{6}\times\dfrac{8}{7}\times\dfrac{9}{8}\times\cdots\times\dfrac{2013}{2012}\times \dfrac{2014}{2013} \times \dfrac{2015}{2014}$

$= \dfrac{2015}{5}$

$> (\dfrac{22}{3})^3$

$\dfrac{6}{5}\times\dfrac{9}{8}\times\cdots\times\dfrac{2010}{2009}\times \dfrac{2013}{2012} > \dfrac{22}{3}$

$\therefore \dfrac{3}{2}\times\dfrac{6}{5}\times\dfrac{9}{8}\times\cdots\times\dfrac{2010}{2009}\times \dfrac{2013}{2012} \ge 11$

$\dfrac{3}{2}\times\dfrac{6}{5}\times\dfrac{9}{8}\times\cdots\times\dfrac{2010}{2009}\times \dfrac{2013}{2012} < 12$ ก็ทำคล้ายๆกันแต่ขั้นนี้ bound ค่ายากมาก

สุดท้ายจะได้คำตอบคือ 11