已知数列an为等差数列且a1=2 a1+a2+a3=12令bn=1/(an+1)(an+3)求bn的前n项和
来源:百度知道 编辑:UC知道 时间:2024/07/02 08:40:00
设公差为d,
a1=2
a1+a2+a3=a1+a1+d+a1+2d=3a1+3d=12
a1+d=4,d=4-2=2,
an=a1+(n-1)*2=2+2(n-1)=2(n+1)
bn=1/(an+1)(an+3)
=1/2*[1/(an+1)-1/(an+3)]
bn的前n项和
Sn=b1+b2+……+bn
=1/2*(1/3-1/5++1/5-1/7+……+1/(an+1)-1/(an+3)]
=1/2*[1/3-1/(an+3))]
=an/6(an+3)
=(n+1)/[3(2n+5)]
S3=3a1+3d=6+3d=12
d=2
bn=1/a(n+1)a(n+3)=1/(2+2n)(2+2(n+2))=1/4(n+1)(n+2)=1/4*[1/(n+1)-1/(n+2)]
S(bn)=1/4*[1/2-1/3+1/3-1/4+……+1/(n+1)-1/(n+2)]
=1/4*[1/2-1/(n+2)]=n/8(n+2)
已知数列{an}是等差数列,且a1=2,a1+a2+a3=12。
已知数列{log2(an-1)}(n属于N*)为等差数列,且a1=3,a3=9,求数列{an}的通项公式.
已知数列{log2(an-1)},(n属于正整数)为等差数列,且a1=3,a3=9,求数列{an}的前n项和Sn
已知数列(an)的前n项和为Sn,首项为a1,且1,an,Sn 成等差数列
已知数列{An}、{Bn}都是公差为1的等差数列,其首项分别为A1、B1,且A1+B1=5,
已知数列an是等比数列,且a1,a2,a4成等差数列,求数列an的公比
已知数列{An}的首项a1=1,其前n项和为Sn,且对任意的正整数n,有n,An,Sn成等差数列
已知数列{log2 (an-1)}为等差数列,且a1=3 a3=9 (1)求an (2)证明1/(a2-a1)+1/(a3-a2)+…+1/a(n+1)-an<1
已知数列前n项和Sn=n(a1+an)/2,如何证明该数列为等差数列
已知数列a1,a2,a3为等比数列,数列a2,a3,a4为等差数列,且a1+a4=16,a2+a3=12,求a1,a2,a3,a4=?