设 _(1)=10, _(n+1)=sqrt (6+{a)_(n)} 证明:极限liman存在,并求之.

102.设 _(1)=4 ,_(n+1)=sqrt ({a)_(n)+2}, 证明:liman存在,并求此极限.

6.设x_(1)=sqrt(6),x_(n+1)=sqrt(6+x_(n))(n=1,2,...),证明数列x_{n)}收敛，并求出极限值.6.设$x_{1}=

5.证明数列 √6, sqrt (6+sqrt {6)}, √(6+√6+√6),······ 的极限存在并求之.[答案:3]

9.设x_(1)=sqrt(2),x_(n+1)=sqrt(2+x_(n))(n=1,2,...),试证数列(x_{n)}极限存在,并求此极限.9.设$x_{1

9.设x_(1)=sqrt(2),x_(n+1)=sqrt(2+x_(n))(n=1,2,...),试证数列(x_(n))极限存在,并求此极限.9.设$x_{1

9.设x_(1)=sqrt(2),x_(n+1)=sqrt(2+x_(n))(n=1,2,...),试证数列(x_{n)}极限存在,并求此极限.9.设$x_{1

【例】求极限lim_(ntoinfty)((1)/(n+1)+(1)/(n+sqrt(2))+...+(1)/(n+sqrt(n)))。【例】求极限$\lim_

).-|||-(1)证明:limxn存在,并求该极限.-|||-n→∞-|||-(2)计算 lim _(narrow infty )((dfrac {{x)_(

求极限lim_(ntoinfty)(sqrt[n]((n+1)(n+2)...(n+n)))/(n).求极限$\lim_{n\to\infty}\frac{\s

设数列|x_(n)|满足：x_(1)in(0,pi)，x_(n+1)=sin x_(n)(nin N_(+)).证明lim_(ntoinfty)x_(n)存在，