Modul
e
9 : Infinite Series, Tests of Convergence, Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture
26 : Conditional convergence [Section 26.2]
(iv)
.
3.
Show that the following series are conditionally convergent:
(i)
.
(ii)
.
(iii)
.
(iv)
.
4.
Prove the following statements:
(i)
If a series
is absolutely convergent, then
.
(ii)
If the series
and
are both absolutely convergent, then so are the series
and
.
5.
Let
series. Define for all
,
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
.
.
.
.
.
is absolutely convergent, then 
.
and 
are both absolutely convergent, then so are the series 
. 
series. Define for all 
, 
