1.已知数列{an}的前四项和等于4,设前n项和为Sn,且n≥2时,an=1/2(根号Sn+根号Sn-1),求S10
问题描述:
1.已知数列{an}的前四项和等于4,设前n项和为Sn,且n≥2时,an=1/2(根号Sn+根号Sn-1),求S10
答
an=Sn-Sn-1=1/2(根号Sn+根号Sn-1)
(根号Sn-根号Sn-1)(根号Sn+根号Sn-1)=Sn-Sn-1
根号Sn-根号Sn-1=1/2
根号Sn为等差数列 且根号S2=2 公差d=1/2
根号S10=根号S2+0.5*6=5
S10=25