若数列{an}满足a1=2且an+an-1=2n+2n-1,Sn为数列{an}的前n项和,则log2(S2012+2)等于(  ) A.2013 B.2012 C.2011 D.2010

问题描述:

若数列{an}满足a1=2且an+an-1=2n+2n-1,Sn为数列{an}的前n项和,则log2(S2012+2)等于(  )
A. 2013
B. 2012
C. 2011
D. 2010

∵an+an-1=2n+2n-1
∴an=2n,即数列{an}是公比q=2的等比数列,
则Sn=

2•(1−2n)
1−2
=2n+1-2,
则S2012=22013-2,
则log2(S2012+2)=log222013=2013,
故选:A.