在数列{an}中a1=1,当n≥2时,an,Sn,Sn-1/2成等比数列.
题目
在数列{an}中a1=1,当n≥2时,an,Sn,Sn-1/2成等比数列.
问:证明{1/Sn}是等差数列.
答案
因为an,Sn,Sn-1/2成等比数列
Sn(平方)=an*(Sn-1/2)
由an=Sn-S(n-1)
Sn(平方)=(Sn-S(n-1))*(Sn-1/2)
化简得S(n-1)*Sn=S(n-1)/2-Sn/2
两边同时除以S(n-1)*Sn
1/Sn-1/S(n-1)=2
{1/Sn}是等差数列
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