(理科)已知数列{an}的前n项和为Sn,a1=-2,an+1=1-1an,则S2013的值为( ) A.6716 B.−6716 C.6713 D.−6713
问题描述:
(理科)已知数列{an}的前n项和为Sn,a1=-2,an+1=1-
,则S2013的值为( )1 an
A.
671 6
B. −
671 6
C.
671 3
D. −
671 3
答
∵数列{an}的前n项和为Sn,a1=-2,an+1=1-
,1 an
∴a2=1−
=1 −2
,3 2
a3=1−
=1
3 2
,1 3
a4=1−
=-2,1
1 3
∴数列{an}是周期为3的周期数列,
∴S2013=671(-2+
+3 2
)=-1 3
.671 6
故选:B.