若两个等差数列{an}{bn}的前n项和分别为An、Bn,且满足An/Bn=(4n+2)/(5n-5)(,则a5+a13)/(b5+b13)的值为 答案是7/8
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![若两个等差数列{an}{bn}的前n项和分别为An、Bn,且满足An/Bn=(4n+2)/(5n-5)(,则a5+a13)/(b5+b13)的值为 答案是7/8](/uploads/image/z/12886543-55-3.jpg?t=%E8%8B%A5%E4%B8%A4%E4%B8%AA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E5%88%86%E5%88%AB%E4%B8%BAAn%E3%80%81Bn%2C%E4%B8%94%E6%BB%A1%E8%B6%B3An%2FBn%3D%284n%2B2%29%2F%285n-5%29%28%2C%E5%88%99a5%2Ba13%29%2F%28b5%2Bb13%29%E7%9A%84%E5%80%BC%E4%B8%BA+%E7%AD%94%E6%A1%88%E6%98%AF7%2F8)
若两个等差数列{an}{bn}的前n项和分别为An、Bn,且满足An/Bn=(4n+2)/(5n-5)(,则a5+a13)/(b5+b13)的值为 答案是7/8
若两个等差数列{an}{bn}的前n项和分别为An、Bn,且满足An/Bn=(4n+2)/(5n-5)(,则a5+a13)/(b5+b13)的值为 答案是7/8
若两个等差数列{an}{bn}的前n项和分别为An、Bn,且满足An/Bn=(4n+2)/(5n-5)(,则a5+a13)/(b5+b13)的值为 答案是7/8
因为an,bn是等差数列
所以
(a5+a13)/(b5+b13)
=A17/B17
=(4*17+2)/(5*17-5)
=70/80
=7/8
如仍有疑惑,欢迎追问.祝:
设an的公差为d,得
∵a5+a13=(a9-4d)+(a9+4d)=2a9;同理b5+b13=2b9
∴(a5+a13)/(b5+b13)=2a9/2b9=a9/b9
∵An/Bn=(4n+2)/(5n-5)
∴(a5+a13)/(b5+b13)=(4×9+2)/(5×9-5)=38/40=19/20
答案为19/20