问题标题:
(2013•山东)设等差数列{an}的前n项和为Sn,且S4=4S2,a2n=2an+1.(Ⅰ)求数列{an}的通项公式;(Ⅱ)设数列{bn}满足b1a1+b2a2+…+bnan=1-12n,n∈N*,求{bn}的前n项和Tn.
问题描述:
(2013•山东)设等差数列{an}的前n项和为Sn,且S4=4S2,a2n=2an+1.
(Ⅰ)求数列{an}的通项公式;
(Ⅱ)设数列{bn}满足
秦无莫回答:
(Ⅰ)设等差数列{an}的首项为a1,公差为d,由S4=4S2,a2n=2an+1得:4a1+6d=8a1+4da1+(2n−1)d=2a1+2(n−1)d+1,解得a1=1,d=2.∴an=2n-1,n∈N*.(Ⅱ)由已知b1a1+b2a2+…+bnan=1-12n,n∈N*,得:当n=1时,b1a...
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