若數列{an}滿足a1=2且an+an-1=2n+2n-1,Sn為數列{an}的前n項和,則log2(S2012+2)等於() A. 2013B. 2012C. 2011D. 2010

若數列{an}滿足a1=2且an+an-1=2n+2n-1,Sn為數列{an}的前n項和,則log2(S2012+2)等於() A. 2013B. 2012C. 2011D. 2010

∵an+an-1=2n+2n-1,∴an=2n,即數列{an}是公比q=2的等比數列,則Sn=2•(1−2n)1−2=2n+1-2,則S2012=22013-2,則log2(S2012+2)=log222013=2013,故選:A.