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=S(n-1)-Sn=[√S(n-1)+√Sn]*[√S(n-1)-√Sn]=1/2（根号Sn+根号Sn-1),
√S(n-1)-√Sn=1/2
数列{√Sn}是等差数列，公差d=1/2 S4=4 √S4=√S1+3d=2 √S1=1/2
√Sn=√S1+(n-1)d=n/2
Sn=n^2/4
S10=100/4=25
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