设数列{an}中,Sn是其前n项和,若首项a1=1,且满足2Sn^2=an(2Sn-1),(n为下标),(n∈N*,n≥2),求通项.

问题描述:

设数列{an}中,Sn是其前n项和,若首项a1=1,且满足2Sn^2=an(2Sn-1),(n为下标),(n∈N*,n≥2),求通项.

利用an=Sn-S(n-1)代入已知,变形得:1/Sn-1/S(n-1)=2从而知{1/Sn}是以1/S1=1/a1=1为首项,公差为2的等差数列∴1/Sn=1+2(n-1)=2n-1∴Sn=1/(2n-1)∴an=Sn-S(n-1)=1/(2n-1)-1/1/(2n-3)=-2/[(2n-...