已知數列{an}的前n項和Sn=+2n,Tn=1/(a1a2)+1/(a2a3)+1/(a3a4)+…+1/(anan+1),求Tn

已知數列{an}的前n項和Sn=+2n,Tn=1/(a1a2)+1/(a2a3)+1/(a3a4)+…+1/(anan+1),求Tn

Sn=n²;+2n是吧.n=1時,a1=S1=1²;+2×1=3n≥2時,an=Sn-S(n-1)=n²;+2n-[(n-1)²;+2(n-1)]=2n+1n=1時,a1=2×1+1=3,同樣滿足通項公式數列{an}的通項公式為an=2n+11/[ana(n+1)]=1/[(2n+1)(2(n+1)+ 1)]=(1/2)…