数列an的前n项和Sn且满足Sn=4/3an-1/3*2^n+1+2/3
问题描述：
数列an的前n项和Sn且满足Sn=4/3an-1/3*2^n+1+2/3
,1)求数列的首项a1与通项Sn(2)设数列bn=2^n/Sn的前项和为Tn求证Tn
数学人气：486 ℃时间：2020-03-22 01:31:08
优质解答
(1)n=1时,a1=S1=(4/3)a1-(1/3)·2²+2/3解得a1=2n≥2时,an=Sn-S(n-1)=(4/3)an -(1/3)·2^(n+1) +2/3-[(4/3)a(n-1)-(1/3)·2ⁿ+2/3]整理,得an=4a(n-1)+2ⁿan+2ⁿ=4a(n-1)+2^(n+1)=4a(n-1)+4·2^(n...
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答
(1)n=1时,a1=S1=(4/3)a1-(1/3)·2²+2/3解得a1=2n≥2时,an=Sn-S(n-1)=(4/3)an -(1/3)·2^(n+1) +2/3-[(4/3)a(n-1)-(1/3)·2ⁿ+2/3]整理,得an=4a(n-1)+2ⁿan+2ⁿ=4a(n-1)+2^(n+1)=4a(n-1)+4·2^(n...