已知数列{an}的前N项和为Sn与an满足:an,Sn,Sn-1/2(n大于2)成等比数列,且a1=1,求Sn

问题描述:

已知数列{an}的前N项和为Sn与an满足:an,Sn,Sn-1/2(n大于2)成等比数列,且a1=1,求Sn

因为an,Sn,Sn-1/2成等比数列所以an*Sn-1/2=Sn^2因为an=Sn-Sn-1所以(Sn-Sn-1)*Sn-1=2Sn^2等式两边同除以Sn^2得[1-(Sn-1/Sn)](Sn-1/Sn)=2令t=Sn-1/Sn则(1-t)t=2 得t=2或t=-1所以Sn是等比数列 且S1=1 公比为-1或2所...