设等差数列{an}的前n项和为Sn,bn=1/Sn,且a3b3=1/2,S5+S3=21

等差数列{an}的前n项和为Sn,bn=1/Sn,且a3b3=1/2
a3b3=a3/S3=a3/(a1+a2a+a3)=1/2
∴a1+a2=a3,公差d=a1,an=n·a1
S5+S3=15a1+6a1=21a1=21
∴a1=1,an=n,Sn=n(n+1)/2,bn=2/n(n+1)
第二题a1=1,a2=2a1/(a1+2)=2/3,a3=2a2/(a2+2)=1/2
1/an=[a(n-1)+2]/2a(n-1)=1/2 + 1/a(n-1)
=1/2 + 1/2 + 1/a(n-2)
∴｛1/an｝成等差数列
1/an=(1+n)/2,an=2/(1+n)

设等差数列{an}的前n项和为Sn,bn=1/Sn,且a3b3=1/2，S5+S3=21(1)求bn (2) 求bn的前2项和Tn
b3=1/s3=1/(a1+a2+a3)=1/(3a1+3d)
a3=a1+2d
s3=3a1+3d
s5=5a1+10d
a3b3=1/(3a1+3d)*(a1+2d)=1/2 (1)
S5+S3=(3a1+3d)+...

看图不解释

(1)等差数列{an}的前n项和为Sn,bn=1/Sn,且a3b3=1/2
a3b3=a3/S3=a3/(a1+a2a+a3)=1/2
∴a1+a2=a3,公差d=a1,an=n·a1
S5+S3=15a1+6a1=21a1=21
∴a1=1,an=n,Sn=n(n+1)/2,bn=2/n(n+1)
(2)b1=1,b2=1/3
Tn估计是bn前n项...