Question

Cho: 0 < a₁ < a₂ < ... < a₉

CMR: \(\frac{a_1+a_2+a_3+...+a_9}{a_3+a_6+a_9}< 3\)

Answer 1

ta có: \(a_1+a_2+a_3< a_3+a_3+a_3\Rightarrow a1+a2+a3< a3.3\)

\(a4+a5+a6< a6+a6+a6\Rightarrow a4+a5+a6< a6.3\)

\(a7+a8+a9< a9+a9+a9\Rightarrow a7+a8+a9< a9.3\)

\(\Rightarrow\frac{a1+a2+a3+...+a9}{a3+a6+a9}< a3.3+a6.3+a9.3\)  ( vì a3 ; a6; a9 >0 )

\(\Rightarrow\frac{a1+a2+a3+...+a9}{a3+a6+a9}< 3.\left(a3+a6+a9\right)\)

\(\Rightarrow a1+a2+a3+...+a9< 3\)

\(\Rightarrow\frac{a1+a2+a3+...+a9}{a3+a6+a9}< 3\left(đpcm\right)\)

CHÚC BN HỌC TỐT!!!!!