Ch12 Infinite Sequence and Series

1
Ch12Infinite Sequence and Series

• ???????

2

• 12.1 ????
• 12.2 ????
• 12.3 ?????
• 12.4 ?????
• 12.5 ????
• 12.6 ??????????????????
• 12.8 ????
• 12.9 ?????????
• 12.10 Taylor ? Maclaurin??

3
12.6 ?????????????????
4
????

• ??????????????
• ?????????????????
• ???????????????????
• ???????????????????

5
???????

• ?San???
• ????
• ? San??,?San????
• ????????????????
• ????
• ? San??,?San????
• ????????????????

6
????
7
Example 1
?
??
??
P-Series, p2
-??
??
??
8
Q1
?

1. Series is absolutely convergent.
2. Series is conditionally convergent.
3. Series is divergent.

9
Q1
?
??
??
P-Series, p1
-??
????
10
Q 2

1. Series is absolutely convergent.
2. Series is conditionally convergent.
3. Series is divergent.

11
Q 2

1. Series is absolutely convergent.

12
??

• ? San????,?San??

13
Example 4
?
?
??
P-Series, p2

• ??????

-??
??
??
14
?????

• ?????
• Ratio Test
• ????San?? n! ? n???
• ??
• ??
• (1) ?lt 1 ? San ??
• (2) ?gt 1 ? San ??
• (3) ? 1 ? San ???

??
15
Example 4
-??
??
n
n
n
n
- ??
8
16
Q 3
?

1. Series is convergent.
2. Series is divergent.

17
Q 3
?
- ??
n
n
n
18
- ??
-??
??
19
?????

• ?????
• Root Test
• ????San?? n???
• ??
• ??
• (1) ?lt 1 ? San ??
• (2) ?gt 1 ? San ??
• (3) ? 1 ? San ???

??
20
Example 6
- ??
-??
??
21
????
???? ???
???? ?????
????
p -?? ?????
???????
???????
???? ?????
?????
22
Figure 8.2.