等差数列An,Bn的前n项合分别为Sn和Tn,若Sn/Tn=2n/3n+1,求An/Bn的表达式.
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![等差数列An,Bn的前n项合分别为Sn和Tn,若Sn/Tn=2n/3n+1,求An/Bn的表达式.](/uploads/image/z/10331014-22-4.jpg?t=%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97An%2CBn%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%90%88%E5%88%86%E5%88%AB%E4%B8%BASn%E5%92%8CTn%2C%E8%8B%A5Sn%2FTn%3D2n%2F3n%2B1%2C%E6%B1%82An%2FBn%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F.)
等差数列An,Bn的前n项合分别为Sn和Tn,若Sn/Tn=2n/3n+1,求An/Bn的表达式.
等差数列An,Bn的前n项合分别为Sn和Tn,若Sn/Tn=2n/3n+1,求An/Bn的表达式.
等差数列An,Bn的前n项合分别为Sn和Tn,若Sn/Tn=2n/3n+1,求An/Bn的表达式.
S(2n-1)=(A1+A(2n-1))×(2n-1)/2
=(A1+A1+(2n-2)d)×(2n-1)/2
=(A1+(n-1)d)×(2n-1)
=An×(2n-1)
同理T(2n-1)=Bn×(2n-1)
Sn/Tn=2n/(3n+1)
将上式中的n换成2n-1
S(2n-1)/T(2n-1)=2(2n-1)/(3(2n-1)+1)=(4n-2)/(6n-2)=(2n-1)/(3n-1)
An/Bn=(An×(2n-1))/(Bn×(2n-1))
=S(2n-1)/T(2n-1)
=(2n-1)/(3n-1)
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