设数列an的前n项和为sn,且a1=1,an+1=2sn+1,数列bn满足a1=b1,点p(bn,bn+1)在直线x-y+2=0上,n是正整数.求an,bn的通项公式.设cn=bn/an,求cn的前n项和tn

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设数列an的前n项和为sn,且a1=1,an+1=2sn+1,数列bn满足a1=b1,点p(bn,bn+1)在直线x-y+2=0上,n是正整数.求an,bn的通项公式.设cn=bn/an,求cn的前n项和tn

设数列an的前n项和为sn,且a1=1,an+1=2sn+1,数列bn满足a1=b1,点p(bn,bn+1)在直线x-y+2=0上,n是正整数.求an,bn的通项公式.设cn=bn/an,求cn的前n项和tn
设数列an的前n项和为sn,且a1=1,an+1=2sn+1,数列bn满足a1=b1,点p(bn,bn+1)在直线x-y+2=0上,n是正整数.
求an,bn的通项公式.设cn=bn/an,求cn的前n项和tn

设数列an的前n项和为sn,且a1=1,an+1=2sn+1,数列bn满足a1=b1,点p(bn,bn+1)在直线x-y+2=0上,n是正整数.求an,bn的通项公式.设cn=bn/an,求cn的前n项和tn
a(n+1)=2Sn+1仿写
an=2S(n-1)+1 相减得a(n+1)=3an a(n+1)/an=3 a1=1 an=3^(n-1)
根据题意bn-b(n+1)+2=0 移项 b(n+1)=bn+2
仿写 bn=b(n-1)+2
b(n-1)=b(n-2)+2
.
b3=b2+2
b2=b1+2
全相加
得 b(n+1)=b1+2n=2n+1 bn=2n-1
cn=(2n-1)/3^(n-1)
tn=1/1+3/3+5/9+7/27+.+(2n-1)/3^(n-1)
1/3tn=1/3+3/9+5/27+7/81+.+(2n-1)/3^n
错位相减得2/3tn=1+2/3+2/9+2/27+.+2/3^(n-1)-(2n-1)/3^n
=1+2*(1/3+1/9+1/27+.+1/3^(n-1))-(2n-1)/3^n
差不多了,剩下的自己应该能求了
OK

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