证明:若a1>a2>……>an,则1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)大于等于0

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 14:27:44
证明:若a1>a2>……>an,则1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)大于等于0证明:若a1>a2>……>an,则1^2/(

证明:若a1>a2>……>an,则1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)大于等于0
证明:若a1>a2>……>an,则1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)大于等于0

证明:若a1>a2>……>an,则1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)大于等于0
若n=2
左边=1/(a1-a2)+4/(a2-a1)=3
1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)>=0
即证1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)>=n^2/(a1-an)
由柯西不等式
(a1-a2+a2-a3+...+an-1-an)[1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)]>=(1+2+..+n-1)^2
即1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)>=(n(n-1)/2)^2/(a1-an)
(n(n-1))^2/[4(a1-an)]>=(2^2*n^2)/[4(a1-an)]=n^2/(a1-an)
所以1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)>=n^2/(a1-an)
原不等式得证

毫无疑问啊,所有指数函数是不可能小于0的
任何一项都是大于0的,你的题目可能写错了

证明:若a1>a2>……>an,则1^2/(a1-a2)+2^2/(a2-a3)+……+(n-1)^2/(an-1-an)+n^2/(an-a1)大于等于0 已知数列{an}中满足a1=1,a(n+1)=2an+1 (n∈N*),证明a1/a2+a2/a3+…+an/a(n+1) 已知a1+a2+…….+an=1求证:a1^2/(a1+a2) + a2^2/(a2+a3)…….+an-1^2/(an-1+an) +an^2/(an+a1)>1/2已知a1+a2+…….+an=1求证:a1^2/(a1+a2) + a2^2/(a2+a3)……+an-1^2/(an-1+an) +an^2/(an+a1)>1/2 等比数列{an}中,a1+ a2+...+ an=2^n-1,则a1^2+a2^2+…+an^2等于多少 设a1,a2,...,an都是正数,证明不等式(a1+a2+...+an)[1/(a1)+1/(a2)+...+1/(an)]>=n^2 【高中数学证明题一道】设a1>a2>…>an>an+1,求证1/(a1-a2)+1/(a2-a3)+…+1/(an-an+1)+1/(an+1-a1)>0.设a1>a2>…>an>an+1,求证1/(a1-a2)+1/(a2-a3)+…+1/(an-an+1)+1/(an+1-a1)>0.最好能用上柯西不等式或均值不等式。 已知数列{an}满足a1=1/2,a1+a2+……+an=n^2an,用数学归纳法证明an=1/{n(n+1)} 一直数列{An}满足A1=1/2,A1+A2+…+An=n^2An用数学归纳法证明An=1/[n(n+1)] 已知数列{An}满足A1=0.5,A1+A2+…+An=n^2An(n∈N*),试用数学归纳法证明:An=1/n(n+1) 证明恒等式a1/a2(a1+a2)+a2/a3(a2+a3)+……+an/a1(an+a1)=a2/a1(a1+a2)+a3/a2(a2+a3)+……+a1/an(an+a1)其中1,2,3,n均为字母a的右下角的小数字.要步骤的(肯定的吧)一定要对的,对的话再加分(我至少懂一点的) 数列题文科已知数列{an}中,a1=1 a2=2,an+1=2an=3an-1 证明数列 an+an+1是等比数列,2 求a1+a2+……+an 数列an满足a1=1/2,a1+a2+a3……an=n^2an,则an 用数学归纳法证明:(a1+a2+…+an)^2=a1^2+a2^2+…a3^3+2(a1a2+^用数学归纳法证明:(a1+a2+…+an)^2=a1^2+a2^2+…an^2+2(a1a2+a1a3+…an-1an). {an}是等比数列.若极限(a1+a2+……+an)=极限(a1^2+a2^2+……+an^2)=2,则a1=? 若数列{an}满足a1=1,an+1=2an,n=1,2,3,……,则a1+a2+……+an=____________ 数列an=n^2 Tn=1/a1 +1/a2 +1/a3+……+1/an 证明Tn 数列an=3^n - 2^n 证明:对一切正整数n 有1/a1 + 1/a2 +…+ 1/an 若数列{an}满足:a1=1,an+1=2an,n=1,2,3….则a1+a2+…+an=______.