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.

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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.
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.

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.
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

∵an+2a(n+1)+a(n+2)=0 设公比为q ∴an+2an·q+an·q²=0
可得 q²+2q+1=0 得q=-1 又a1=2
S(2010)=2·(1-(-1)2010)/1-(-1)
=0