Module 1
:
Real Numbers, Functions and Sequences
Lecture
2
:
Convergent & Bounded Sequences [ Section 2.3 : Bounded Sequences ]
2.3.3
Theorem:
If
is convergent then it is bounded.
Proof:
Let
. Then given
, say
= 1, there exists
such that
That means all
's, accept
lie in between
- 1 and
+ 1. Thus, if we define
Hence,
is bounded.
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is convergent then it is bounded.
, say 
= 1, there exists 
such that 
's, accept 
lie in between 
- 1 and 
+ 1. Thus, if we define
