再写一个式子a(n+1)+1=1/2(a1+^+a(n+1))与条件式相减可得a(n+1)-an=1/2a(n+1)an=1/2(an+1)当n=1时a1+1=1/2a1a1=-1/2a1不等于0所以为等比数列an=-(1/2)^nSn=[-1/2+(1/2)^(n+1)]/(1+1/2)=1/3*(1/2)^n-1/3综上所述Sn=1/3*(1/2)^n-1/3
