数列an中 a1=1 当n大于等2时 其前n项和满足sn2=an(sn-1/2) 求sn an
问题描述:
数列an中 a1=1 当n大于等2时 其前n项和满足sn2=an(sn-1/2) 求sn an
答
an=Sn-S(n-1)所以Sn²=[Sn-S(n-1)](Sn-1/2)=Sn²-S(n-1)Sn-1/2*Sn+1/2*S(n-1)所以-S(n-1)Sn-1/2*Sn+1/2*S(n-1)=0S(n-1)Sn=1/2*Sn-1/2*S(n-1)两边除以S(n-1)Sn1=1/2*[Sn-S(n-1)]/[S(n-1)Sn]所以2=1/Sn-1/S(n-...