an》0,an+1/an=2Sn.求数列{an}
问题描述:
an》0,an+1/an=2Sn.求数列{an}
答
a1=1,由上面得:Sn-Sn1+1/(Sn-Sn-1)=2Sn,化简得:Sn*Sn-Sn-1*Sn-1=1,得到一个等差数列,求出Sn*Sn=n,则an=根号n-根号(n-1)
an》0,an+1/an=2Sn.求数列{an}
a1=1,由上面得:Sn-Sn1+1/(Sn-Sn-1)=2Sn,化简得:Sn*Sn-Sn-1*Sn-1=1,得到一个等差数列,求出Sn*Sn=n,则an=根号n-根号(n-1)