20.设a_(n)=int_(0)^1x^nsqrt(1-x^2)dx(n=0,1,2,...),则lim_(ntoinfty)((a_(n))/(a_(n-2)))^n=_.

9.设a_(n)=int_(0)^1x^nsqrt(1-x^2)dx,b_(n)=int_(0)^(pi)/(2)sin^ntdt,则极限lim_(ntoinf

9.设a_(n)=int_(0)^1x^nsqrt(1-x^2)dx,b_(n)=int_(0)^(pi)/(2)sin^ntdt,则极限lim_(ntoinf

设A_(1),A_(2),...,A_(n),...是事件列，若A_(n)subset A_(n+1),n=1,2,...,A=bigcap_(i=1)^inf

【例14】设a_(1)+a_(2)+...+a_(n)=0，求证：方程na_(n)x^n-1+(n-1)a_(n-1)x^n-2+...+2a_(2)x+a_(

(3)设a_(n)>0(n=1,2,...),S_(n)=a_(1)+a_(2)+...+a_(n),则数列S_(n)有界是数列a_(n)收敛的A. 充分必要条

2 给出以下4个命题①若lim_(ntoinfty)a_(n)=a，则当n充分大时，|a_(n)-a|0，当n充分大时，|a_(n)-a|0，当n充分大时，|a

若lim_(ntoinfty)a_(n)=0，则(a_{n)}必为单调递减序列。A. 对B. 错

2、设级数sum_(n=1)^inftya_(n)收敛，lim_(ntoinfty)na_(n)=a.证明：sum_(n=1)^inftyn(a_(n)-a_(

4.设A_(2n-1)=(0,(1)/(n)),A_(2n)=(0,n),n=1,2,….求出集列(A_{n)}的上限集和下限集.4.设$A_{2n-1}=\l

4.设A_(2n-1)=(0,(1)/(n)),A_(2n)=(0,n),n=1,2,···,求出集列A_(n)的上限集和下限集.4.设$A_{2n-1}=(0