已知ai∈R+,且a1+a2+...ai=1 求证:(a1+1/a1)^2+(a2+1/a2)^2+...+(an+1/an)^2>=(n^2+1)^2/n用柯西不等式等式右边为[(n^2+1)^2]/n
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/30 00:36:41
![已知ai∈R+,且a1+a2+...ai=1 求证:(a1+1/a1)^2+(a2+1/a2)^2+...+(an+1/an)^2>=(n^2+1)^2/n用柯西不等式等式右边为[(n^2+1)^2]/n](/uploads/image/z/14879363-59-3.jpg?t=%E5%B7%B2%E7%9F%A5ai%E2%88%88R%2B%2C%E4%B8%94a1%2Ba2%2B...ai%3D1+%E6%B1%82%E8%AF%81%3A%28a1%2B1%2Fa1%29%5E2%2B%28a2%2B1%2Fa2%29%5E2%2B...%2B%28an%2B1%2Fan%29%5E2%3E%3D%28n%5E2%2B1%29%5E2%2Fn%E7%94%A8%E6%9F%AF%E8%A5%BF%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%AD%89%E5%BC%8F%E5%8F%B3%E8%BE%B9%E4%B8%BA%5B%28n%5E2%2B1%29%5E2%5D%2Fn)
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来源:学生作业帮助网 编辑:作业帮 时间:2024/07/30 00:36:41