已知正项数列{An}满足Sn+Sn-1=tAn^2+2(n>=2,t>0),A1=1,其中Sn是数列{An}的前n项和.1.求通项An2.记数列{1/AnAn+1}的前n项和为Tn,若TnIwannanobodynobodybut

Question

已知正项数列{An}满足Sn+Sn-1=tAn^2 +2(n>=2,t>0),A1=1,其中Sn是数列{An}的前n项和.
1.求通项An
2.记数列{1/AnAn+1}的前n项和为Tn,若Tn
I wanna nobody nobody but

Answer 1

Sn+Sn-1=tAn^2 +2
Sn-1+Sn-2=tAn-1^2 +2
两式相减
An+An-1=t(An^2-An-1^2)
1=t(An-An-1)
是等差数列.
An=（n+t-1)/t
1/AnAn+1 = t (1/An - 1/An+1)
Tn= t (1/A1 - 1/An+1) = t （1 - t/(n+t) )
An是递增正项数列.Tn是递增数列.
要使Tn