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)^inftyA_(i),则有P(A)=lim_(ntoinfty)P(A_(n)).（判断10分）

3.[判断题]设A_(1),A_(2),...,A_(n)为n个事件，若对任意的i，j(1≤i，j≤n)，均有P(A_(i)A_(j))=P(A_(i))P(A

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_(

(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

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

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

9.(2025·全国一卷·高考真题)设数列(a_{n)}满足a_(1)=3,(a_(n+1))/(n)=(a_(n))/(n+1)+(1)/(n(n+1))(1

(6)设a_(1),a_(2),a_(3),a_(4)是n维向量，a_(1),a_(2)线性无关，a_(1),a_(2),a_(3)线性相关，且 a_(1)+a

3.设A=(a_(ij))_(ntimes n)，如果A的元素满足 |a_(ii)|>sum_(j=1jneq i)^n|a_(ij)| (i=1,2,...,

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