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Ch12 Infinite Sequence and Series

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Ch12 Infinite Sequence and Series 12.1 12.2 12.3 12.4 12.5 12.6 ... – PowerPoint PPT presentation

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Title: 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
12.2Infinite Series
  • ????

4
????
  • ?????????
  • ?????????????????
  • ???????????????????????????
  • ???????????
  • ??????????????????

5
????
????????
6
????
?
7
?
????
S1 a1
S1 a1
S2 a1 a2
S3 a1 a2 a3
Sn a1 a2 a3 an


8
????
n
n
n

8
S8
9
????
  • S1, S2, S3, , Sn ,
  • ???????
  • ?????
  • S1, S2, S3, , Sn , , S8

S8
S
10
????
  • ???? ? ????
  • ? ????
  • ???? ? ????
  • ? ????

11
????
???? Series ??? Tests
???? Geometric S. ????? Divergence T.
???? Telescoping S.
????????????
12
????
  • ???? Geometric Series
  • ?? a ar ar2 arn
  • ?? a, ?? r
  • ??
  • r lt 1 ? ?????? a/1-r
  • r ? 1 ? ?????? 8

13
Example 2
?? 5, ?? -2/3
?? -2/3 lt 1 ? ?????? -2/3 ? 1 ?
??????
14
Q 1(3/6)
?
?? 1/9, ?? 1/3
?? 1/3 lt 1 ? ?????? 1/3 ? 1 ?
??????
15
Example 3
gt1
Diverges !!!
16
Example 4 Write the number as a ratio of
integers.
??
??
17
Example 5 where x lt 1.
r x lt 1, it converges
18
????
  • ???? Telescoping Series
  • ??
  • ? Sn
  • ? lim Sn , n?8

19
Example 6
?
  • ? Sn

?
?
  • ? lim Sn , n?8

20
Q 2
(a) ??
(b) 3/2
(c) 1
(d) 0
21
????
  • ????? Divergence Test
  • ??









a2
a3
an
a1
?????








??,
? 0
22
????
  • ????? Divergence Test
  • ??

?
?0 ????
23
????
  • ????? Divergence Test
  • ????San
  • ?? lim an
  • ??
  • ?? lim an ? o ? San??

??
24
Q 3
(a) ??
(b) ??
(c) 8
(d) 0
-??
-??
- ??
??
25
Example 8
-??
-??
- ??
??
26
Q 4 (Eg. 9)
(a) ??
(b) 3/2
(c) 1
(d) 4
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