问题 选择题 已知函数f(x)=1-x,x<1x-1,x≥1,若数列{an}满足a1=3,an+1=f(an),n∈N*,数列{an}前n项和为Sn,则S2010-2S2009+S2008=( )A.1B.0C.-1D.-2 答案 由题意,a1=3,a2=2,a3=1,a4=0,a5=1,a6=0,a7=1,…∴S2010-2S2009+S2008=5+1004-2(5+1003+1)+(5+1003)=-1故选C.