已知数列{an}是各项均不为0的等差数列,公差为d,Sn为其前n项和,且满足an^2=S2n-1,n∈N*,数列{bn}满足bn=1/(an·an+1),Tn为数列{bn}的前n项和.(1)求a1、d、和Tn(2)若对任意的n属于N*,不等式λTn
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![已知数列{an}是各项均不为0的等差数列,公差为d,Sn为其前n项和,且满足an^2=S2n-1,n∈N*,数列{bn}满足bn=1/(an·an+1),Tn为数列{bn}的前n项和.(1)求a1、d、和Tn(2)若对任意的n属于N*,不等式λTn](/uploads/image/z/5453071-7-1.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E6%98%AF%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%8D%E4%B8%BA0%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E5%85%AC%E5%B7%AE%E4%B8%BAd%2CSn%E4%B8%BA%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8C%2C%E4%B8%94%E6%BB%A1%E8%B6%B3an%5E2%3DS2n-1%2Cn%E2%88%88N%2A%2C%E6%95%B0%E5%88%97%EF%BD%9Bbn%EF%BD%9D%E6%BB%A1%E8%B6%B3bn%3D1%2F%28an%C2%B7an%2B1%29%2CTn%E4%B8%BA%E6%95%B0%E5%88%97%EF%BD%9Bbn%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C.%281%29%E6%B1%82a1%E3%80%81d%E3%80%81%E5%92%8CTn%282%29%E8%8B%A5%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%9A%84n%E5%B1%9E%E4%BA%8EN%2A%2C%E4%B8%8D%E7%AD%89%E5%BC%8F%CE%BBTn)
已知数列{an}是各项均不为0的等差数列,公差为d,Sn为其前n项和,且满足an^2=S2n-1,n∈N*,数列{bn}满足bn=1/(an·an+1),Tn为数列{bn}的前n项和.(1)求a1、d、和Tn(2)若对任意的n属于N*,不等式λTn 已知数列{an}是各项均不为0的等差数列,公差为d,Sn为其前n项和,且满足an^2=S2n-1,n∈N*,数列{bn}满足bn=1/(an·an+1),Tn为数列{bn}的前n项和.(1)求a1、d、和Tn(2)若对任意的n属于N*,不等式λTn Sn=na1+[n(n-1)d]/2,所以an²=S(2n-1)=(2n-1)a1+(n-1)(2n-1)d,化简得到an=0,或者an=2n-1,如题an均不为0,所以an=1,且d=2.
已知数列{an}是各项均不为0的等差数列,公差为d,Sn为其前n项和,且满足an^2=S2n-1,n∈N*,数列{bn}满
足bn=1/(an·an+1),Tn为数列{bn}的前n项和.
(1)求a1、d、和Tn
(2)若对任意的n属于N*,不等式λTn
an²=S2n-1
a1²=S1
a1=1、0
数列{an}是各项均不为0的=>
a1=1
an²=S2n-1
a2²=S3=a3+a2+a1
(a1+d)²=a1+2d+a1+d+a1
d²+2d+1=3d+3
d²-d-2=0
d=2、-1
数列{an}是各项均不为0的=>a2!=1-1=>
d=2
bn=1/(an·an+1)(n+1是角标吧?不是就别往下看了-.-b)
=1/[(2n-1)·(2n+1)]
=[1/(2n-1) - 1/(2n+1)]/2
Tn=1/2 · [1/1-1/3 + 1/3-1/5 +...+1/(2n-1) - 1/(2n+1)]
=1/2 · [1 - 1/(2n+1)]
=n/(2n+1)
(2):
λTn