等差数列{an},{bn}的前项分别为Sn和Tn ,Sn/Tn=2n/(3n+1)求a8/b8
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等差数列{an},{bn}的前项分别为Sn和Tn ,Sn/Tn=2n/(3n+1)求a8/b8
由等差数列的性质:a15+a1=2(a8),同理b15+b1=2(b8),
{an}的前15项和为S15=(a1+a15)*15/2,
{bn}的前15项和为T15=(b1+b15)*15/2,
S15/T15=a8/b8=(2*15)/(3*15+1)=15/23 (这行看不懂,
由等差数列的性质:a15+a1=2(a8),同理b15+b1=2(b8),
{an}的前15项和为S15=(a1+a15)*15/2,
{bn}的前15项和为T15=(b1+b15)*15/2,
S15/T15=a8/b8=(2*15)/(3*15+1)=15/23 (这行看不懂,
S15/T15= ((a1+a15)*15/2)/((b1+b15)*15/2)
= (a15+a1)/(b1+b15)
由等差数列的性质:a15+a1=2(a8),同理b15+b1=2(b8),
所以S15/T15=a8/b8
又因为Sn/Tn=2n/(3n+1)
所以S15/T15=(2x15)/(3x15+1)=15/23
所以a8/b8=15/23
= (a15+a1)/(b1+b15)
由等差数列的性质:a15+a1=2(a8),同理b15+b1=2(b8),
所以S15/T15=a8/b8
又因为Sn/Tn=2n/(3n+1)
所以S15/T15=(2x15)/(3x15+1)=15/23
所以a8/b8=15/23
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