- 一道不等式的证明，急急急！！！！！！！！在线等设ai∈R+(i=
- 设ai∈R+(i=1,2,3……n),a1+a2+……+an=1,求证∑(ai+1/ai)^2≥（n^2+1）^2/n
- 可用Cauchy不等式证明:
∵ai∈R+,且∑ai=1,
故有,
∑(1/ai)=∑ai×∑(1/ai)≥n^2 (Cauchy不等式)
∴n×∑(ai+1/ai)^2
≥[∑(ai+1/ai)]^2 (Cauchy不等式)
=[∑ai+∑(1/ai)]^2
=[∑ai+∑ai×∑(1/ai)]^2
≥(1+n^2)^2
两边除以n,得
∴∑(ai+1/ai)≥(1+n^2)^2/n.
注:为方便手机表达,以上省略了∑的上、下标.