Question

已知数列{an}的前n项和Sn=（（an+1）/2）的平方,当an＞0时,Sn=?

Answer 1

当n>=2 ,an=Sn-S(n-1)=（（an+1）/2)^2-（（a(n-1)+1）/2)^2,所以(an+a(n-1))(an-a(n-1)-2)=0,an+a(n-1)=0或an-a(n-1)-2=0.因为an>0,an-a(n-1)=2,an=2n-1,Sn=n^2