高中数列难题A1=3/2,An=3nA(n-1)/[2A(n-1)+(n-1)]∴n/An=2/3+(n-1)/3A(n-1),设Bn=n/An,则Bn=(2/3)+B(n-1)/3,Bn-1=[B(n-1)-1]/3,∴数列{Bn-1}是首项B1-1=1/A1-1=-1/3,公比q=1/3的等比数列,通项Bn-1=(-1/3)·(1/3)^(n-1),Bn=1-(1/3)^n∴An=n/B
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 15:17:16
![高中数列难题A1=3/2,An=3nA(n-1)/[2A(n-1)+(n-1)]∴n/An=2/3+(n-1)/3A(n-1),设Bn=n/An,则Bn=(2/3)+B(n-1)/3,Bn-1=[B(n-1)-1]/3,∴数列{Bn-1}是首项B1-1=1/A1-1=-1/3,公比q=1/3的等比数列,通项Bn-1=(-1/3)·(1/3)^(n-1),Bn=1-(1/3)^n∴An=n/B](/uploads/image/z/1389217-49-7.jpg?t=%E9%AB%98%E4%B8%AD%E6%95%B0%E5%88%97%E9%9A%BE%E9%A2%98A1%3D3%2F2%2CAn%3D3nA%28n-1%29%2F%5B2A%28n-1%29%2B%28n-1%29%5D%E2%88%B4n%2FAn%3D2%2F3%2B%28n-1%29%2F3A%28n-1%29%2C%E8%AE%BEBn%3Dn%2FAn%2C%E5%88%99Bn%3D%282%2F3%29%2BB%28n-1%29%2F3%2CBn-1%3D%5BB%28n-1%29-1%5D%2F3%2C%E2%88%B4%E6%95%B0%E5%88%97%7BBn-1%7D%E6%98%AF%E9%A6%96%E9%A1%B9B1-1%3D1%2FA1-1%3D-1%2F3%2C%E5%85%AC%E6%AF%94q%3D1%2F3%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E9%80%9A%E9%A1%B9Bn-1%3D%28-1%2F3%29%C2%B7%281%2F3%29%5E%28n-1%EF%BC%89%2CBn%3D1-%281%2F3%29%5En%E2%88%B4An%3Dn%2FB)
xT[kA+Bˮdf?RKm'i1(B(}7Rri<"T||9ofїnf:}ڰI[ܤܒ'QIG'FQ>~}lsS$[e(1{̊۰ P+$r;}#Kl*b2`tz:ZSt3>Zm,J#mA h v_3奢.:9]yZt^DirTWjs}ͭ,TЃr+V.B/Θ8q20l1#\#N~c4\'Nyv
VkyIKrCiS1