一道等差数列的题目不会做题目:设等差数列{an},{bn}的前n项和分别为Sn和Tn.(1)求证:an/bn=(S2n-1)/(T2n-1) (2)若Sn/Tn=(5n+1)/(3n-1),求a3/b3的值

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一道等差数列的题目不会做题目:设等差数列{an},{bn}的前n项和分别为Sn和Tn.(1)求证:an/bn=(S2n-1)/(T2n-1) (2)若Sn/Tn=(5n+1)/(3n-1),求a3/b3的值
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一道等差数列的题目不会做题目:设等差数列{an},{bn}的前n项和分别为Sn和Tn.(1)求证:an/bn=(S2n-1)/(T2n-1) (2)若Sn/Tn=(5n+1)/(3n-1),求a3/b3的值
一道等差数列的题目不会做
题目:设等差数列{an},{bn}的前n项和分别为Sn和Tn.(1)求证:an/bn=(S2n-1)/(T2n-1) (2)若Sn/Tn=(5n+1)/(3n-1),求a3/b3的值

一道等差数列的题目不会做题目:设等差数列{an},{bn}的前n项和分别为Sn和Tn.(1)求证:an/bn=(S2n-1)/(T2n-1) (2)若Sn/Tn=(5n+1)/(3n-1),求a3/b3的值
(1)证明:令{an}的公差为d1,{bn}的公差为d2.
则S2n-1=[a1+a1+(2n-1-1)d1](2n-1)/2=2[a1+(n-1)d1](2n-1)/2
T2n-1=[b1+b1+(2n-1-1)d2](2n-1)/2=2[b1+(n-1)d2](2n-1)/2
(S2n-1)/(T2n-1)=[a1+(n-1)d1]/[b1+(n-1)d2]=an/bn
(2)由上知a3/b3=S5/T5=(5n+1)/(3n-1)=13/7.

a3/b3=13/8

13/7