设等差数列{an}的前n项和为Sn 若a1=Sn>

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设等差数列{an}的前n项和为Sn 若a1=Sn>
设等差数列{an}的前n项和为Sn 若a1=Sn
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设等差数列{an}的前n项和为Sn 若a1=Sn>
1.S2013=(a1+a2013)*2013/2=0
a1+a2013=0 a10
所以 d>0
a1+a2013=2a1007=0
a1007=0
前1006项都为负数,所以S1006最小,n=1006
2.a2013=a1+2012d=0
a1=-2012d
Sn=na1+n(n-1)d/2=-2012nd+n(n-1)d/2
an=a1+(n-1)d=-2013d+nd
an-Sn
=-2013d+nd+2012nd-n(n-1)d/2
=2013d(n-1)-n(n-1)d/2
=d(n-1)(2013-n/2)
=d/2(n-1)(4026-n)>=0 d>0
(n-1)(n-4026)

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