(习题解答)习题9常数项级数收敛性的判定.pdf
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1、1/14 习题 9-2 1.判断下列级数的敛散性.1);2);3);4);5);6)解:1);方法一:利用正项级数的比较判别法)因为,而调和级数发散,从而也发散;由正项级数的比较判别法,得级数发散。方法二:利用正项级数的比较判别法的极限形式)因为,而调和级数发散,则由正项级数的比较判别法的极限形式,得级数发散。2);方法一:利用正项级数的比较判别法)因为,而级数收敛 级数的结论);由正项级数的比较判别法,得级数收敛。方法二:利用正项级数的比较判别法的极限形式)因为,而级数收敛 级数的结论),2/14 则由正项级数的比较判别法的极限形式,得级数收敛。3);方法一:利用正项级数的比较判别法)因为)
2、,且调和级数发散;则由正项级数的比较判别法,得级数发散。方法二:利用正项级数的比较判别法的极限形式)因为,而,所以,即,又调和级数发散,则由正项级数的比较判别法的极限形式,得级数发散。4);方法一:利用正项级数的比较判别法)因为,而级数收敛级数的结论),由正项级数的比较判别法,得级数收敛。方法二:利用正项级数的比较判别法的极限形式)文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX
3、7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T
4、4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB
5、8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E
6、4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 Z
7、O5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X
8、3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文
9、档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K23/14 因为,而级数收敛 级数的结论),则由正项级数的比较判别法的极限形式,得级数收敛。5);因为,而调和级数发散,则由正项级数的比较判别法的极限形式,得级数发散。注:本题中,级数的一般项要进行适当的缩小不易,所以采用正项级数的比较判别法做起来相对比较困难一些,而采用正项级数的比较判别法的极限形式相对容易一些。6)当时,则由级数收敛的必要条件,得级数)发散;当时,则由级数收敛的必要条件,得级数)发散;当时,且级数是公比为)的等比
10、级数,是收敛的,则由正项级数的比较判别法的极限形式,得级数收敛。文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1
11、 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1
12、W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z1
13、0 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R
14、10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4
15、K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码
16、:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K24/14 综上,当时,级数发散;当时,级数收敛。2.判断下列级数的敛散性.1);2);3);4);5);
17、6);7);8);9);10);11)其中,均为正数).解:1);方法一:利用正项级数的比较判别法)因为,且收敛,由正项级数的比较判别法,得级数收敛。方法二:利用正项级数的比较判别法的极限形式)因为,且级数收敛,由正项级数的比较判别法的极限形式,得级数收敛。2);方法一:利用正项级数的比较判别法的极限形式)文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8
18、G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4
19、Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO
20、5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3
21、Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档
22、编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7
23、A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4
24、M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K25/14 因为,且等比级数收敛,由正项级数的比较判别法的极限形式,得级数收敛。方法二:利用正项级数的比值判别法)因为,由正项级数的比值判别法,得级数收敛。3);因为),而,利用级数收敛性的结论,得当即时 级数是发 散的;当即时 级 数是收敛的;由正项级数的比较判别法的极限形式,得当时级数发散;当时级数收敛。文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R
25、10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4K2文档编码:CX7A6D2T4M1 HB8G1W9E4Z10 ZO5R10X3Y4
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