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.

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

设数列x_{n)}满足：x_(1)>0,x_(n)e^x_(n+1)=e^x_(n)-1(n=1,2,...).证明x_{n)}收敛，并求极限lim x_(n)

(45)设数列x_{n)}满足x_(1)=1,x_(n+1)=(x_(n)+2)/(x_(n)+1)(n=1,2,...),试证lim_(ntoinfty)x_

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，

设数列x_{n)}由x_(1)in(-infty,+infty)和x_(n+1)=(1)/(3)x_(n)+(2)/(3)-(1)/(2)int_(1)^x_(

5.设 0le x_(1)le sqrt(c),x_(n+1)=(c(1+x_(n)))/(c+x_(n)),nin Z^+,c>1.证明数列x_{n)}收敛，

(级数 第15届非数A初赛)设数列(x_{n)}满足x_(0)=(1)/(3)，x_(n+1)=(x_(n)^2)/(1-x_(n)+x_{n)^2},ngeq

注：类似地，设数列x_{n)}由x_(1)in(-infty,+infty)和x_(n+1)=(1)/(3)x_(n)+(2)/(3)-(1)/(2)int_(