【摘要】 研究离散形式的加权几何平均不等式,证明了对任何非负数列{a_n},不等式（?） （?）v_ka_k成立的充分必要条件是对任意n（?）1,有1/n（?）C₂,其中u_n（?）0,v_n＞0,C₁,C₂为常数．更多还原

【Abstract】 A discrete weighted geometric average inequality is studied and it is proved that then inequality sum from k=1 to∞uk （a₁…a_k）^1/k≤C₁ sum from k=1 to∞v_ka_k holds for all nonnegative sequence {a_n} if and only if there holds 1/n sum from k=1 to∞u_k/（v₁…v_k）^1/k≤C₂ for all n≥1,where u_n≥0,v_n＞0 and C₁,C₂ are constants.更多还原