若数列{an}满足a1=2且an+an-1=2n+2n-1,Sn为数列{an}前n项和,则log2(S2012+2)=_.
若数列{an}满足a1=2且an+an-1=2n+2n-1,Sn为数列{an}前n项和,则log2(S2012+2)=______.
数学人气:996 ℃时间:2020-04-22 20:59:43
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∵an+an-1=2n+2n-1,Sn为数列{an}前n项和,∴S2012=(a1+a2)+(a3+a4)+…+(a2011+a2012)=(21+22)+(23+2⁴)+…+(22011+22012)=2+22+23+…+22012=2(1−22012)1−2=22013-2,∴S2012+2=22013,∴log2(S2012+...
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