Question

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.

Answer 1

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)