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

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

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

4.设f在[a,b]上有界，(a_{n)}⊂[a,b]，lim_(ntoinfty)a_(n)=c.证明：若f在[a,b]上只有a_(n)（n=1,2,...）

3 已知数列(a_{n)}(a_(n)≠0),若(a_{n)}发散,则A. $a_{n}+\frac{1}{a_{n}}$发散.B. $a_{n}-\frac{

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

2 已知数列 a_{n)} (a_(n) neq 0)，若 a_{n)} 发散，则（）A. $\{a_{n} + \frac{1}{a_{n}}\}$ 发散B.

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

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.[填空题]若lim_(ntoinfty)x_(n)=alpha，则lim_(ntoinfty)|x_(n)|=____.3.[填空题]若$\lim_{n\t