Module 1
:
Real Numbers, Functions and Sequences
Lecture
3
:
Monotone Sequence and Limit theorem [ Section 3.1 : Monotone Sequences ]
Practice Exercises 3.1: Monotone Sequences
(1)
Determine whether the sequences are increasing or decreasing:
(2)
Show that the following sequences are convergent by showing that they are monotone and bounded. Find their limits also:
(i)
(ii)
(iii)
(3)
Let
and
.
Show that
is a decreasing sequence,
is an increasing sequence and
for every
.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
and 
. 
is a decreasing sequence, 
is an increasing sequence and 
for every 
. 
