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

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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.

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