数列{an}的通项公式为an=2nsin(nπ/2-π/3)+√3ncos(nπ/2),前n项和为Sn,则S2012=

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数列{an}的通项公式为an=2nsin(nπ/2-π/3)+√3ncos(nπ/2),前n项和为Sn,则S2012=
答案是-1006

an=2nsin(nπ/2-π/3)+√3ncos(nπ/2)
=2n[ (1/2)sin(nπ/2)-(√3/2)cos(nπ/2)] +√3ncos(nπ/2)
= nsin(nπ/2)
an = n if n=1,5,9,...
= 0 if n=2,4,6,8,10,.
= -n if n=3,7,11,.
S2012 = a1+a2+...+a2012
= (1+5+9+...+2009)-(3+7+9+...+2011)
= (1+2009)503/2 -(3+2011)503/2
=-503(2)
=-1006

数列{an}的通项公式为an=2nsin(nπ/2-π/3)+√3ncos(nπ/2),前n项和为Sn,则S2012= 数列{an}的通项公式为an=2nsin(nπ/2-π/3)+√3ncos(nπ/2),前n项和为Sn, 数列{an}的通项公式an=ncos(nπ/2),其前n项和为Sn,则S2012等于（） A.1006 B.2012 数列An的通向公式An=ncos(nπ/2)+1其前n项和为Sn,则S2012=? 数列｛an｝的通项公式an=ncos(nπ/2)+1,前n项和为Sn,则S2014=? 数列{an}的通项公式an=cos[(nπ)/2],其前n项和为Sn,则S2012等于已知数列{an}的通项公式an=ncos(nπ/3),其前n项和为Sn,则S2014等于数列an的通项公式an＝ncosnπ/2+1,前n项和为sn,则s2012＝已知数列an的前n项和为Sn,a1=1,当n>=2时,an+2Sn-1=n,则S2012等于已知数列{An}的前n项和为Sn,且满足Sn=2An-3n(n属于N+) 1.求{An}的通项公式 3 数列｛an｝的通项公式an=(-1)^(n-1)*2n(n属于N*)设其前n项和为Sn,则S100= 设等比数列{an}的前n项和为Sn,已知a1=2011,且an+2an+1+an+2=0(N∈N*),则S2012?