已知a1+a2+……+an=n×n×n,求:1/(a2-1)+1/(a3-1)+1/(a4-1)+……+1/(a2011
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/10/05 01:13:35
已知a1+a2+……+an=n×n×n,求:1/(a2-1)+1/(a3-1)+1/(a4-1)+……+1/(a2011-1)=?
∵a1+a2+……+an=n×n×n
∴an=n^3-(n-1)^3=n^2+n*(n+1)+(n+1)^2=n^2+(n^2+n)+(n^2+2n+1)=3n^2+3n+1
1/(an-1)=1/(3n^2+3n+1-1)=1/(3n*(n+1))=1/3*[1/n - 1/(n+1)]
1/(a2-1)+1/(a3-1)+1/(a4-1)+……+1/(a2011-1)
=1/3*{(1/2 - 1/3)+(1/3 - 1/4)+(1/4 - 1/5)+……(1/2011 - 1/2012)}
=1/3*(1/2 - 1/2012)
=1/3*(2012-2)/(2012*2)
=335/2012
∴an=n^3-(n-1)^3=n^2+n*(n+1)+(n+1)^2=n^2+(n^2+n)+(n^2+2n+1)=3n^2+3n+1
1/(an-1)=1/(3n^2+3n+1-1)=1/(3n*(n+1))=1/3*[1/n - 1/(n+1)]
1/(a2-1)+1/(a3-1)+1/(a4-1)+……+1/(a2011-1)
=1/3*{(1/2 - 1/3)+(1/3 - 1/4)+(1/4 - 1/5)+……(1/2011 - 1/2012)}
=1/3*(1/2 - 1/2012)
=1/3*(2012-2)/(2012*2)
=335/2012
已知a1+a2+……+an=n×n×n,求:1/(a2-1)+1/(a3-1)+1/(a4-1)+……+1/(a2011
已知数列{an}满足a1+a2+a3+...+an=n^2+2n.(1)求a1,a2,a3,a4
已知a1=x,an+1=1-1/an(n=1,2,3,…)求a2,a3,a4,a5:;求a2002
已知a1=x,an+1=1-1/an(n=1,2,3,…)求a2,a3,a4,a5;求a2002
已知n系正整数,an=1*2*3*4*.n,则a1/a3+a2/a4+a2010/a2012+a2011/2013=
已知数列{an}前n项的和Sn=n的平方+12n,求和a1-a2+a3-a4+…+(-1)的(n+1)次方·an
已知数列{an}满足:a1=1,且an-a(n-1)=2n.求a2,a3,a4.求数列{an}通项an
已知数列{an}中,a1+a2+a3+……+an=3^n-2^n/2^n(n=1,2,……)求证{an}是等
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
数列(an)满足啊a1+2a2+3a3+4a4+……+nan=n(n+1)(n+2)(n≥2且n为自然数)求an的通项公
已知数列an= n-1 (n为奇数) n (n为偶数) 则a1+a2+a3+a4+…+a99+a100=?
设a1,a2,a3,…,an(n∈N*)都是正数,且a1a2a3•…an=1,试用数学归纳法证明:a1+a2+a3+…+