等比数列{an},a1=2,an+2a(n+1)+a(n+2)=0则S(2010)=?括号里的均为下标.
问题描述：
等比数列{an},a1=2,an+2a(n+1)+a(n+2)=0则S(2010)=?括号里的均为下标.
答
等比数列{an},a1=2,an+2a(n+1)+a(n+2)=0,
an+2an *q+an *q²=0
1+2q+q²=0
q=-1
an=2*(-1)^(n-1)
S(2010)=2-2+2-2+.+2-2=0