(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-

1
an
,则S2013的值为(  )
A.
671
6

B.
671
6

C.
671
3

D.
671
3

∵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−
1
1
3
=-2,
∴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.