由正数组成的等差数列an和bn的前n项和分别为sn和tn,且sn比tn=2n比3n+1,则a5比b7=?
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由正数组成的等差数列an和bn的前n项和分别为sn和tn,且sn比tn=2n比3n+1,则a5比b7=?
由正数组成的等差数列an和bn的前n项和分别为sn和tn,且sn比tn=2n比3n+1,则a5比b7=?
由正数组成的等差数列an和bn的前n项和分别为sn和tn,且sn比tn=2n比3n+1,则a5比b7=?
∵Sn/Tn=2n/(3n+1)
{an},{bn}为等差数列,公差不是0
令Sn=2n*kn =2kn²
Tn=(3n+1)*kn=3kn²+kn (将约去的n的倍数补回来)
n≥2时,an=Sn-S(n-1)=2k[n²-(n-1)²]=2k(2n-1)
bn=Tn-T(n-1)=k[3n²+n-3(n-1)²-(n-1)]
=k(6n-2)
∴a5/b7=2k×9/[k×40)=9/20
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