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_(1)^x_(n)e^-t^(2)dt(n=1,2,...)所确定证明：极限lim_(ntoinfty)x_(n)存在并求此极限.

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_(

(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)>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)

(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

(3)设X_(1)sim N(1,2),X_(2)sim N(0,3),X_(3)sim N(2,1),且X_(1),X_(2),X_(3)相互独立，则P0le

1 设总体Xsim N(0,1)，X_(1),X_(2),...,X_(n)为X的样本，则((X_(1)-X_(2))/(X_(3)+X_{4)})^2服从__

设X_(1),X_(2),...,X_(n)为总体Xsim N(mu,sigma^2)的样本，证明hat(mu)_(1)=(1)/(2)X_(1)+(2)/(3

6、设X_(1)sim N(1,2)，X_(2)sim N(0,3)，X_(3)sim N(2,1)，且X_(1),X_(2),X_(3)独立，则P(0le 2

12.设x_(1),x_(2),...,x_(n),x_(n+1)是来自N(mu,sigma^2)的样本，overline(x)_(n)=(1)/(n)sum_

设x_(0)=0,x_(n)=(1+2x_(n-1))/(1+x_(n-1))(n=1,2,3,...),则lim_(ntoinfty)x_(n)=设$x_{0