设{An}是等差数列,{Bn}是各项都为正数的等比数列,且A1=B1=1,A3+B5=21,A5+B3=13(1)求{An},{Bn}的通项公式;(2)求数列{An/Bn}的前n项和Sn`
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![设{An}是等差数列,{Bn}是各项都为正数的等比数列,且A1=B1=1,A3+B5=21,A5+B3=13(1)求{An},{Bn}的通项公式;(2)求数列{An/Bn}的前n项和Sn`](/uploads/image/z/8961695-71-5.jpg?t=%E8%AE%BE%7BAn%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%7BBn%7D%E6%98%AF%E5%90%84%E9%A1%B9%E9%83%BD%E4%B8%BA%E6%AD%A3%E6%95%B0%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E4%B8%94A1%3DB1%3D1%2CA3%2BB5%3D21%2CA5%2BB3%3D13%EF%BC%881%EF%BC%89%E6%B1%82%7BAn%7D%2C%7BBn%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97%7BAn%2FBn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%60)
设{An}是等差数列,{Bn}是各项都为正数的等比数列,且A1=B1=1,A3+B5=21,A5+B3=13(1)求{An},{Bn}的通项公式;(2)求数列{An/Bn}的前n项和Sn`
设{An}是等差数列,{Bn}是各项都为正数的等比数列,且A1=B1=1,A3+B5=21,A5+B3=13
(1)求{An},{Bn}的通项公式;
(2)求数列{An/Bn}的前n项和Sn
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设{An}是等差数列,{Bn}是各项都为正数的等比数列,且A1=B1=1,A3+B5=21,A5+B3=13(1)求{An},{Bn}的通项公式;(2)求数列{An/Bn}的前n项和Sn`
1.设an=a1+(n-1)d=1+(n-1)d
bn=b1*q^(n-1)=q^(n-1)
a3+b5=1+2d+q^4=21 ①
a5+b3=1+4d+q^2=13 ②
联立①②得q^2=4
因为{bn}各项为正数
所以q=2 则d=2
an=2n-1
bn=2^(n-1)
2.an/bn=(2n-1)/[2^(n-1)]=(4n-2)/2^n=(4n/2^n)-(2/2^n)
设cn=4n/2^n dn=2/2^n前N项和为Cn,Dn
Cn=4/2+4*2/2^2+4*3/2^3...+4n/2^n ①
1/2Cn=4/2^2+4*2+2^3+...+4(n-1)/2^n+4n/2^(n+1) ②
①-②得1/2Cn=4/2+4/2^2+4/2^3+...+4/2^n-4n/2^(n+1)
=2{[1-(1/2)^n]/(1-1/2)}-4n/2^(n+1)=4[1-(1/2)^n]-4n/2^(n+1)
Dn=2/2+2/2^2+2/2^3+...+2/2^n[1-(1/2)^n]/(1-1/2)=2[1-(1/2)^n]
Sn=Cn-Dn=2[1-(1/2)^n]-4n/2^(n+1)
截图看吧,不然不好显示那些公式。
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