设正数a1 a2 a3 ,…,an an+1 成等差数列………求大神解题啊.

来源：学生作业帮助网编辑：六六作业网时间：2024/12/23 11:34:04

设正数a1a2a3,…,anan+1成等差数列………求大神解题啊.设正数a1a2a3,…,anan+1成等差数列………求大神解题啊. 设正数a1a2a3,…,anan+1成等差数列………求大

设正数a1 a2 a3 ,…,an an+1 成等差数列………求大神解题啊.
设正数a1 a2 a3 ,…,an an+1 成等差数列………求大神解题啊.

全部展开

因为a1、a2、a3、......an、a(n+1)成等差数列，设其公差为d
则a2-a1=d a3-a2=d.............a(n+1)-an=d
所以
1/(√a1+√a2)+1/(√a2+√a3)+.......+1/(√an+√a(n+1))
=(√a1-√a2)/(a1-a2)+(√a2-√a3)/(a2-a3)+...........+(√an-√a(n+1))/(an-a(n+1))
=-(√a1-√a2)/d-(√a2-√a3)/d+...........-(√an-√a(n+1))/d
=(-1/d)[(√a1-√a2)+(√a2-√a3)+...........+(√an-√a(n+1))]
=(-1/d)(√a1-√a(n+1))
=(√a(n+1)-√a1)/d
=(√a(n+1)-√a1)/(a(n+1)-a1)
=1/(√a(n+1)+√a1)
于是命题得证

收起

设a1,a2……an为正数, ,求证(a1a2)/a3+(a2a3)/a1 +(a3a1)/a2>=a1+a2+a3 设a1,a2,.an是正数.求证a2 /(a1+a2)^2+a3/(a1+a2+a3)^2+.+an/(a1+a2+.+an)^2 设正数a1 a2 a3 ,…,an an+1 成等差数列………求大神解题啊. 设a1,a2,a3.an都是正数,证明不等式(a1+a2+.+an)(1/a1+1/a2+.+1/an)≥n² a1+a2+a3...aN 【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。设数列{an}满足：存在正数M,对一切n有An=|a2-a1|+|a3-a2|+-----+|an-a(n-1)| 已知正数a1,a2,a3...an满足a1*a2*a3*...*an=1.求证：(2+a1)*(2+a2)*(2+a3)*...*(2+an)>=3^n 设a1,a2,...,an都是正数,证明不等式(a1+a2+...+an)[1/(a1)+1/(a2)+...+1/(an)]>=n^2 设a1,a2,a3…an为任意实数证明：cos(a1)*cos(a2)*…cos(an)+sin(a1)*sin(a2)*…sin(an) 设a1,a2,a3…an为任意实数证明：cos(a1)+cos(a2)+…cos(an)+sin(a1)+sin(a2)+…sin(an) 数学题设（an)是公差为正数的等差数列,若A1+A2+A3=15,A1*A2*A3=80.求S33 设｛an｝是公差为正数的等差数列,若a1+a2+a3=15,a1*a2*a3=80,则a11+a12+a13=多少 za zuo a 设a1,a2...an为正数,是分别用柯西不等式与排列不等式证明ai^2/a2+a2^2/a3+...+an^2/a1>=a1+a2+...+an a1 a2 a3……an 都为正数且a1*a2*a3*……*an=1,试用数学归纳法证明a1+a2+a3+………+an>=n 均值不等式的推广式证明a1,a2,a3,……an都是正数,求证：a1+a2+a3+……+an≥n*{n次根号下（a1*a2*a3*……*an）} 设A1,A2,A3…,An是常数（n是大于1的整数,且A1 计算（a1+a2+...+an-1)x(a2+a3+...+an)-(a2+a3+...+an-1)(a1+a2+...+an)