Module 1
:
Real Numbers, Functions and Sequences
Lectur
e
3
:
Monotone Sequence and Limit theorem [ Section 3.2 : Limit Theorems on Sequences ]
3.2.2
Sandwich Theorem:
Let
for all
. If
and
, then
.
Proof
Let
. Using definition, find natural numbers
and
such that
Let
. Then, for
we have
i.e.,
. Thus,
Back
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for all 
. If 
and 
, then 
. 
. Using definition, find natural numbers 
and 
such that
. Then, for 
we have 
. Thus, 
