Sn是等差数列an的前n项和,Bn=1/Sn,a3*b3=0.5,S3+a15=21,求数列bn的前n项和Tn

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Sn是等差数列an的前n项和,Bn=1/Sn,a3*b3=0.5,S3+a15=21,求数列bn的前n项和TnSn是等差数列an的前n项和,Bn=1/Sn,a3*b3=0.5,S3+a15=21,求数

Sn是等差数列an的前n项和,Bn=1/Sn,a3*b3=0.5,S3+a15=21,求数列bn的前n项和Tn
Sn是等差数列an的前n项和,Bn=1/Sn,a3*b3=0.5,S3+a15=21,求数列bn的前n项和Tn

Sn是等差数列an的前n项和,Bn=1/Sn,a3*b3=0.5,S3+a15=21,求数列bn的前n项和Tn
设{an}公差为d.
a3×b3=0.5
a3/S3=1/2
S3-2a3=0
3a1+3d-2(a1+2d)=0
a1-d=0
d=a1
S3+a15=21
3a1+3d+a1+14d=21
4a1+17d=21
d=a1代入,21a1=21
a1=1
d=a1=1
an=1+(n-1)=n
Sn=a1+a2+...+an=1+2+...+n=n(n+1)/2
bn=1/Sn=2/[n(n+1)]=2[1/n -1/(n+1)]
Tn=b1+b2+...+bn
=2[1/1-1/2+1/2-1/3+...+1/n -1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1)

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