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问题: 数列

已知数列{an}中,a1= -2,且an+1=Sn. 求an ; Sn.

解答:

a(n+1)=Sn
an=S(n-1)
a(n+1)-an =an
a(n+1)=2an是等比数列
a1= -2 ===>an =(-2)*2^(n-1) = - 2^n

Sn =-2(1-2^n)/(1-2) = 2 -2^(n+1)