(1).在数列An中,A1=3,且对任意大于1的正整数n,点(根号An,根号An-1)在直线x-y-根号3=0上,则limAn/(n+1)^2=?(2)若两个等差数列An,Bn,的前n项和分别是An,Bn,且满足An/Bn=3n+4/5n-1,则limAn/Bn(3)等比数列An满足
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![(1).在数列An中,A1=3,且对任意大于1的正整数n,点(根号An,根号An-1)在直线x-y-根号3=0上,则limAn/(n+1)^2=?(2)若两个等差数列An,Bn,的前n项和分别是An,Bn,且满足An/Bn=3n+4/5n-1,则limAn/Bn(3)等比数列An满足](/uploads/image/z/14473762-34-2.jpg?t=%281%29.%E5%9C%A8%E6%95%B0%E5%88%97An%E4%B8%AD%2CA1%3D3%2C%E4%B8%94%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%A4%A7%E4%BA%8E1%E7%9A%84%E6%AD%A3%E6%95%B4%E6%95%B0n%2C%E7%82%B9%EF%BC%88%E6%A0%B9%E5%8F%B7An%2C%E6%A0%B9%E5%8F%B7An-1%EF%BC%89%E5%9C%A8%E7%9B%B4%E7%BA%BFx-y-%E6%A0%B9%E5%8F%B73%3D0%E4%B8%8A%2C%E5%88%99limAn%2F%EF%BC%88n%2B1%EF%BC%89%5E2%3D%3F%282%29%E8%8B%A5%E4%B8%A4%E4%B8%AA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97An%2CBn%2C%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E5%88%86%E5%88%AB%E6%98%AFAn%2CBn%2C%E4%B8%94%E6%BB%A1%E8%B6%B3An%2FBn%3D3n%2B4%2F5n-1%2C%E5%88%99limAn%2FBn%283%29%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97An%E6%BB%A1%E8%B6%B3)
(1).在数列An中,A1=3,且对任意大于1的正整数n,点(根号An,根号An-1)在直线x-y-根号3=0上,则limAn/(n+1)^2=?(2)若两个等差数列An,Bn,的前n项和分别是An,Bn,且满足An/Bn=3n+4/5n-1,则limAn/Bn(3)等比数列An满足
(1).在数列An中,A1=3,且对任意大于1的正整数n,点(根号An,根号An-1)在直线x-y-根号3=0上,则limAn/(n+1)^2=?
(2)若两个等差数列An,Bn,的前n项和分别是An,Bn,且满足An/Bn=3n+4/5n-1,则limAn/Bn
(3)等比数列An满足lim(A1+A2+A3+……An)=0.5,那么A1的取值范围是?
(1).在数列An中,A1=3,且对任意大于1的正整数n,点(根号An,根号An-1)在直线x-y-根号3=0上,则limAn/(n+1)^2=?(2)若两个等差数列An,Bn,的前n项和分别是An,Bn,且满足An/Bn=3n+4/5n-1,则limAn/Bn(3)等比数列An满足
[√An - √A(n-1)]在直线x-y-根号3=0上
√An - √A(n-1) - √3 = 0
√An - √A(n-1) = √3
所以√An 为等差数列.公差为 √3.
√An = √A1 + (n-1)d = √3 + (n-1)√3 = n√3
两边平方:
An = 3 n^2
limAn/(n+1)^2=3
an=a1+(n-1)d,bn=b1+(n-1)e,d、e是公差
An/Bn=[2a1+(n-1)d]/[2b1+(n-1)e]
=[dn+(2a1-d)]/[en+(2b1-e)]
=(3n+4)/(5n-1)
对比系数知d/e=3/5
所以limAn/Bn=lim [a1+(n-1)d]/[b1+(n-1)e]=d/e=3/5
a2+a3+…an
=a1*q*(1-q^n)/(1-q)
lim(a2+a3+…an)
=a1*q/(1-q)
如果这个极限存在,那么必定有|q|1/2 或者 1/(2q)0 或者 a1
果然是我们新中的么= =、、那张万恶的数列卷= =