已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=_____,及a9/(b5+b7)+a3/(b4+b8)=______.
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![已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=_____,及a9/(b5+b7)+a3/(b4+b8)=______.](/uploads/image/z/12886527-39-7.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%A4%E4%B8%AA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E5%92%8C%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E5%88%86%E5%88%AB%E4%B8%BAAn%E5%92%8CBn%2C%E4%B8%94An%2FBn%3D%285n%2B3%29%2F%282n-1%29%2C%E5%88%99%E8%BF%99%E4%B8%A4%E4%B8%AA%E6%95%B0%E5%88%97%E7%9A%84%E7%AC%AC%E4%B9%9D%E9%A1%B9%E4%B9%8B%E6%AF%94a9%2Fb9%3D_____%2C%E5%8F%8Aa9%2F%28b5%2Bb7%29%2Ba3%2F%28b4%2Bb8%29%3D______.)
已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=_____,及a9/(b5+b7)+a3/(b4+b8)=______.
已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=_____,及a9/(b5+b7)+a3/(b4+b8)=______.
已知两个等差数列{an}和{bn}的前n项和分别为An和Bn,且An/Bn=(5n+3)/(2n-1),则这两个数列的第九项之比a9/b9=_____,及a9/(b5+b7)+a3/(b4+b8)=______.
A(2n-1)=[a1+a(2n-1)]*(2n-1)/2=(2n-1)an
B(2n-1)=[a1+a(2n-1)]*(2n-1)/2=(2n-1)bn
an/bn=A(2n-1)/B(2n-1)
A17=(a1+a17)*17/2=17a9
B17=(b1+b17)*17/12=17b9
a9/b9=A17/B17
=(5*17+3)/(2*17-1)
=88/33
=8/3
a9/(b5+b7)+a3/(b4+b8)
=a9/(2b6)+a3/(2b6)
=(a9+a3)/(2b6)
=2a6/(2b6)
=a6/b6
=A11/B11
=(5*11+3)/(2*11-1)
=58/21
等差数列,前n项和An,Bn都含n这个因式
设An/Bn约单项式 nk
则An=(5n+3)nk,Bn=(2n-1)nk
an=An-A(n-1)=(10n-2)k
bn=Bn-B(n-1)=(4n-3)k
a9=88k,b9=33k
a9/b9=88/33=8/3
a9/(b5+b7)+a3/(b4+b8)
=88k/(17k+25k)+28k/(13k+29k)
=88k/42k+28k/42k
=116k/42k
=58/21