若无穷数列an满足a1=2,an+1=根号3an+2,且有极限,则liman=

来源：学生作业帮助网编辑：作业帮时间：2024/07/13 09:30:19

x��QMN�@��,�J�n��sM�+��@��V &4�& 5&�^��L�+8b�uw�~��,�ɯ�|m��vł�Gx��y��G�i�� ]�MG�>䏃��`r~v��:�42��p�\E�U`��`��\ �M�^�l @GT0쩆��f�T�2VB�P�P�KL��a�fsѴ��;Բڡ��U�� |1@�f�XR�,6l��i��]�<U��,�˸V��ޮٜ/��T��/��HT�봖_�F�{�s1M?��xѱ�+�#Ny��27

若无穷数列an满足a1=2,an+1=根号3an+2,且有极限,则liman=
若无穷数列an满足a1=2,an+1=根号3an+2,且有极限,则liman=

若无穷数列an满足a1=2,an+1=根号3an+2,且有极限,则liman=
A(n+1) = √3*An + 2
A(n+1) + c = √3*An + 2 + c = √3 * [An + (2+c)/√3 ]
令 c = (2+c)/√3,则 c = 2/(√3 -1) = √3 + 1
所以有：
A(n+1) + √3 + 1 = √3 (An + √3 + 1)
可见,｛An+√3+1｝就是一个等比数列,因此有：
An+√3+1 = (A1 + √3 + 1) * (√3)^(n-1) = (√3+2) * (√3)^(n-1)
所以,An = (√3+2)*(√3)^(n-1) - √3 - 1
limAn 为无穷大.

关于数列极限的已知数列an满足a1=0 a2=1 an=(an-1+an-2)/2 求lim(n->无穷）an 数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an 若无穷数列an满足a1=2,an+1=根号3an+2,且有极限,则liman= 数列{an}满足a1=a,an+1=1+1/an.若3/2 数列{an}满足a1=1 an+1=2n+1an/an+2n 数列an满足a1=2,an+1=4an+9,则an=? 数列｛an｝满足a1=1,且an=an-1+3n-2,求an 已知数列{an}满足an+1=2an+3.5^n,a1=6.求an 数列an满足a1=2,an+1=an²求an 数列an满足a1=2,an+1=an²求an 已知数列{an}满足 n∈N 都有a(n+1)=13an-25／an+3 (1)若a1=5,求an (2)若a1=3,求an (3)a1=6 求an （4）当a1取哪些值时,无穷数列an不存在已知函数f（x）=2-|x|,无穷数列{an}满足an+1=f（an）,n∈N* 若a1=0,求a2,a3,a4；已知函数f（x）=2-|x|,无穷数列{an}满足an+1=f（an）,n∈N*若a1=0,求a2,a3,a4；关于数列、等差数列的题目设数列an满足an+1=an-2且a1=241）判断an是什么数列2）若an 若数列{An},满足关系a1=2,an+1=3an+2,求数列的通项公式若数列【an】满足a1等于1,An+1=2an+3n,则数列的项A5 若数列{an}满足a1=1,a2=5且an+2=an+1-an,求a2000 已知数列{an}满足a1=1 an+1=an/(3an+1) 则球an 数列an满足a1=1/2,a1+a2+a3……an=n^2an,则an